Matter tells matter how to move

[Mentz114]

jon,

I'm focused on one very narrow point here: Whether spatial curvature and spacetime curvature are the actual physical mechanisms by which gravity exercises its effects.

It will be a unicorn hunt. I don't think there's anything in the literature about this.

M

 

[pmb_phy]

Yes I understand, but respectfully disagree with, your position on this matter. :)

I don't follow. Please state what it is you disagree with. Thanks.

Observers in a spacetime without any tidal forces that is a valid solution to Einstein's equations will not observe any gravity.

Seems circular to me since the validity of that statement depends on what is meant by "gravity."

Without a tidal force there will be no gravitation in general relativity at least not in any valid solutions of Einstein's equations.

Huh? Since when? Then again we're back to the definition of "gravity." What is it you're referring to when you speak of "valid solutions of Einstein's equations."?? What does that have to do with the definition of "gravity."

 

[pmb_phy]

Hi Pete,

Well I tend to be dense but I don't quite get your point.

A tidal force relates two particles which are accelerating with respect to each other when each are in free-fall. The gravitational force refers only to the force on one particle relative to the frame of reference. The presence of a gravitational field can be detected with one test particle. The presence of tidal forces requires the use of two test particles.

The gravitational field of spherical massive bodies is of course not "uniform", in the sense that it has two components of tidal gradient.

Two components of tidal gravity? What does that mean?

First, the gravitational potential weakens per the inverse-square law ..

Poential decreases as 1/r. Gravitational force decreases as 1/r^2. And this is the Newtonian approximation. GR is a bit different.

Consider an infintesimal "point" test particle in circular orbit around a stationary spherical massive object with no atmosphere. It certainly feels the mathematical consequences of "spacetime curvature", despite experiencing no tidal gradients.

This is an example of when there is a gravitational force acting on the particle. This force can be transformed away.

So clearly "Gravity = Spacetime Curvature" is an accurate description here.

I don't see how from what you said.

If you change the scenario to add tidal gradients, that's just an additional directional aspect of plain old gravity, nothing fundamentally different.

There is no change in scenario. The tidal gradients didn't go away because you were only looking at one particle.

Pete

 

[MeJennifer]

What is it you're referring to when you speak of "valid solutions of Einstein's equations."?? What does that have to do with the definition of "gravity."

Unless you claim that GR is incomplete only spacetimes that are a solution to Einstein's GR equations are valid, that implies that only matter-free spacetimes are Riemann flat, all other spacetimes must have at least some curvature. Note, in this context, that conformally flat is not equal to Riemann flat.

Einstein's field equations: http://en.wikipedia.org/wiki/Einstein_field_equations

The presence of a gravitational field can be detected with one test particle.

How?

 

[pmb_phy]

Unless you claim that GR is incomplete ...

I've never posted anything on the internet or elsewhere which would indicate, or even hint at me thinking that. Why would you coime to that conclusion?

..only spacetimes that are a solution to Einstein's GR equations are valid, that implies that only matter-free spacetimes are Riemann flat, all other spacetimes must have at least some curvature.

That is not the case. Einstein's field equations imply that, if there is matter at an event P in spacetime then the spacetime curvature at that event is non-zero. That does not imply that the region of spacetime outside the source has a non-zero spacetime curvature.

How?

MJ - There is no use in going into that until you understand what I'm referring to when I use the term "gravity."

Do you have the text Gravitation, by Misner, Thorne and Wheeler? If so then turn to page 467. The authors explain

One can always find in any given locality a frame of reference in which all local "gravitational fields" (all Christoffel symbols; all \Gamma^\alpha_{\mu\nu}) disappear. No \Gamma's means no "gravitational field" ...

Recall the geodesic equation which relates the inertial acceleration of a test particle to the Christoffel symbols and the velocity of the particle. That equatioin implies that if you place a free test particle at a point P in a region of space in the spacetime and the particle accelerates when placed there then there is a gravitational field at that point. This doesn't come as a surprise to you does it?

In Einstein's words

what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the components of the affine connection], not the vanishing of the [components of the Riemann tensor]. If one does not think in such intuitive (anschaulich) ways, one cannot grasp why something like curvature should have anything at all to do with gravitation. In any case, no rational person would have hit upon anything otherwise. The key to the understanding of the equality of gravitational mass and inertial mass would have been missing.

This quote is from General Relativity and Gravitation, Proceedings of the 11th International Conference on General Relativity and Gravitation, (Stockholm,Cambridge University Press, Jul 6-12, 1986), How Einstein Discovered General Relativity: A Historical Tale With Some Contemporary Morals, J.J. Stachel

I have a question for the good folks here: How do you believe that Einstein defined the gravitational field in his published papers on the general theory of relativity. I.e. what mathematical quantities defined the presence of a gravitational field in Einstein's GR papers and his GR book?

Pete

Ps - I'm sending you additional information in PM.

 

[jonmtkisco]

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

 

[Xezlec]

OK, maybe I'm being dense and missing some key part of this conversation.

But I don't see how "gravity's just a plain ol' force" explains the effects that it has on time. Go into a high-gravity environment, and when you come back, your watch will be wrong. And you'll be the wrong age. How is that a force? That's not a force. Someone's a-monkeyin' with time. Time is a dimension. So something really weird is going on.

Right?

If you can brush off time warping, then the rest of what you're saying is probably an argument over language, i.e. "You didn't actually close the door. Clearly, the door simply closed itself to avoid a paradox where the laws of physics were no longer an accurate description." Equivalent statements. The fact that you can phrase it both ways just means English is ambiguous.

 

[jonmtkisco]

Hi Xezlec,

But I don't see how "gravity's just a plain ol' force" explains the effects that it has on time.

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.

Of course, time dilation is a well-established phenomenon of SR, occurring simply due to relative constant velocity between two inertial frames, without requiring the presence of gravity or acceleration. So, what physical "mechanism" causes time dilation, and specifically is it a single mechanism, or is there a different mechanism for gravity than for inertial velocity differentials? The equivalence principle suggests that it is a single mechanism.

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). That seems weird.

"Curved spacetime" loosely describes the observed effects of gravity, but as far as I can see it doesn't explain how gravity's physical mechanism could be the same mechanism as a velocity differential.

Jon

 

[RandallB]

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.

Available online at University of New Mexico
http://info.phys.unm.edu/papers/2000/Fuchs2000a.pdf

It also includes “Reply by Fuchs and Peres” to critical letters, which appeared in Physics Today 53(9), 14,90 (2000).

 

[jonmtkisco]

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).

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.

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.

I don't recall that being said explicitly in the things I've read, so I'd like to confirm it's true.

Jon

 

[RandallB]

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.

Something seems not quite complete or right, but I can't put my finger on what may be missing; maybe someone else can.

 

[jonmtkisco]

The same scenario can be defined more simply as follows:

An observer in a rocket travels straight towards Planet M from a great distance away. The rocket motor is used as necessary to maintain a constant velocity towards Planet M equal to Planet M's escape velocity at its surface.

I predict that the observer's clock will not experience time dilation relative to a clock on the surface of Planet M, and light emitted from the surface of Planet M will not appear at all redshifted to the observer.

Note that since the rocket maintains a constant relative velocity, the observer is not in "freefall" towards Planet M except at the final instant before the rocket contacts the surface.

Jon

 

[jonmtkisco]

Edit: I was going to make another post but I've decided to wait so I can think it through better.

Jon

 

[jonmtkisco]

Here's an amazingly naive question:

As I understand it, the escape velocity from the center of a massive body (such as moon) is equal to \sqrt{1.5} times the escape velocity at the surface.

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.

I'd love to read about it just for the sake of sanity. I use moon as an example because I want to exclude atmospheric resistance. I also want to assume no rotational effects.

Jon

 

[RandallB]

Jon
I’ve considered something like this approach before and IMO it does favor the SM interpretation over the Warped space view.
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. For the SR motion you need to set up the example with a transverse relative motion for the SR observer. That way SR color shifts due to Doppler effects are eliminated and only SR time dilation in the transverse case will remain. Some speed for such a SR observer should match the Gravitational time dilation / red shift to give the observer a dilation and thus cancel out that gravitational red shift for that observer. Let us know if by working the numbers it matches your expectation of escape speed for the source point.

 

[jtbell]

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.

What do you mean by "further accelerated"? 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?

 

[jonmtkisco]

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?

Yes, that's right JT. I know that in all versions of gravitational theory the predicted velocity will be greater than 10 km/s when the object hits the moon. I'm just wondering if anyone has ever specifically tested this scenario, because the answer doesn't become certain until one measures it.

Jon

 

[jonmtkisco]

Hi Randall,

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.

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.

Jon

 

[kahoomann]

Matter can't act on another matter directly. This is what Einstein call "spooky action at a distance".
That's why John Wheeler famously said: "matter tells Spacetime how to curve, and Spacetime tells matter how to move."

 

[jonmtkisco]

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

 

[matheinste]

Helo all.

Quote:-

----A kind of sad example of entrenching oneself in the theory that makes one a celebrity.----

But as he "discovered" relativity surely we can we forgive him for this.

Matheinste

 

[jonmtkisco]

Hi matheinste,
Of course. It doesn't take anything away from his great achievements. I feel a bit sad for him though because he spent most of the rest of his career in a dead-end effort to extend relativity into a geometry-based "theory of everything", at a time when others were making much progress in particle physics.

Jon

 

[Mentz114]

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

Hi Jon,
this is not wholly accurate. I refer to Einstein's 1917 paper ( 12 years after the PE paper) called 'On the Quantum Theory of Radiation' (Phys. Zs. 18 pp121 ) where he establishes that photon emission/absorption entails an exchange of momentum, and introduces spontaneous emission for the first time, and says quite explicitly that is is governed by 'chance'.

What he didn't like about QM is the fact that only probabilities can be calculated. Although, having said that one process is random, how could he expect anything else ?

M

 

[kahoomann]

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

The tenet of Special Relativity is that any interaction must be local. It apply to all physical theory, not just quantum mechanics.
BTY, do you agree with John Wheeler that "matter tells Spacetime how to curve, and Spacetime tells matter how to move."? If yes, why did you change it to "Matter tells matter how to move"?

 

[jonmtkisco]

Hi kahoomann,
Please read the very first post in this thread, where I pose the question whether there is a sound basis for categorically rejecting the possibility that matter acts on matter, rather than acting on "spacetime". IMO spacetime was originally invented by Minkowski as a mathematical aid or analogy, and was not originally accepted as a physical embodiment per se. Certainly Einstein was slow to adopt it as the physical description of gravitational action. It became encrusted over the years with the trappings of a physical embodiment, thanks to enthusiastic relativists like Wheeler and many others.

I'm not taking a categorical stand one way or the other, I just think both avenues should be pursued. GR may hold up as a perfectly accurate mathematical predictor of gravitational action at macro scales even it turns out that it does not literally warp spacetime. It was pointed out elsewhere in this thread that the Graviton theory in QM is probably best described as a mediated force rather than as a true local warping of the universal background geometry.

Jon

 

[RandallB]

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.

Your missing the point Jon
I wasn’t talking about how GR works or how SR works.
I was talking about how your examples work, or actually cannot work as you want.

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 towards or away form each other will give you positional Doppler effect of red or blue shifts.

What your trying to do requires holding distance at a constant to eliminate positional Doppler effects! You need to isolate and only allow the SR transverse Doppler effect in your exsample, in order to only see the effect caused by SR time dilation.

 

[jonmtkisco]

Hi Randall,

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.

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. So unfortunately my attempt to convert gravitational effects into constant velocity effects doesn't work out in the simple way I had hoped.

It would work if the gravitational field were uniform, e.g. if the source were an infinite slab of matter rather than a spherical planet. Spherical geometry really screws up the simplicity of gravity. The complexity is due solely to the fact that all gravitating point particles such as fermions have spherical gravitational symmetry. Spherical particles ==> tidal effects.

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.

Jon

 

[RandallB]

SR vs Gr Time dilation

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.

No your still not on point with what I’m sure I read as your own objective.

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.
With O stationary at some great distance they will observe a gravitational redshift coming from M.
I read your objective as trying to induce a SR time dilation on O to make that observed redshift disappear.
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.

What does “orbital speed can never be fast enough” have to do with it, no one is suggested O needed to be in orbit. Just that it needs to not change distance to M. It can follow an orbital path or just make the observation when its tangent path touches a circular orbit point.
Of course the speed of O will need to be higher than any orbital speed to achieve a SR time dilation equivalent to the gravitational time dilation, but it will certainly be less than “c” as well.

So as I said, there is one fixed speed for O that will match the time dilation of M, at that speed the transverse Doppler effect will cause O to see the light from M with no transverse red/blue shift at all.

The question is what is that one speed for O.
And how does it compare with your guess that it may be related to escape velocity at the light source point on M surface.
I won’t have time to crunch those numbers for awhile, but that is what you need for the example you posed.

 

[jonmtkisco]

Hi Randall,

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.

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. It definitely is not; relativistic Doppler shift completely incorporates and subsumes Classic Doppler shift within it. Classical Doppler effect is just a simpler way of calculating relativistic Doppler effect which is accurate at low speeds and increasingly inaccurate as the speed of light is approached. The specific correction that relativistic Doppler effect makes to the classical calculation is to factor in a Lorentz boost to account for the time dilation.

From the Wikipedia article on Redshift:

"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 \gamma into the classical Doppler formula...

Jon

 

[RandallB]

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.

Not at all.
It's just that it should be very clear when the observer has radial motion towards or away from the planet they can in no way be considered in the same refrerance frame as the source of light your trying to make comarisions with. Referance frame differances are not what you were proposeing to compare.
Therefore it should be clear the radial Doppler effect is a problem and must be eliminated to make the time dilation to time dilation comparisons you are attempting.
Sounds simple because it is that simple.