Matter tells matter how to move

[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.

 

[jonmtkisco]

Hi Randall,

Referance frame differances are not what you were proposeing to compare.

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.

Jon

 

[RandallB]

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.

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.

Apparently you are evidently unwilling to even consider that approach.
Or it might be I have completely misunderstood your original objective.
Either way this discussion as passed any productive purpose,
I’ll unsubscribe from the thread so you may continue with your own line of reasoning.

 

[jonmtkisco]

Hi Randall,
I'm willing to consider transverse Doppler, but it made sense to me that we get straight on the meaning of radial Doppler first. Sorry the discussion didn't work out.

Jon

 

[atyy]

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=g_ijdxⁱdx^j" gives the Riemannian metric in terms of the Euclidean metric.

 

[kahoomann]

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=g_ijdxⁱdx^j" gives the Riemannian metric in terms of the Euclidean metric.

What does this, flat or curved, has anything to do with "Matter tells matter how to move"?
The tenet of special relativity is that any interaction must be local. So the "Matter tells matter how to move" is some kind of "spooky action at a distance" due to Einstein

 

[jonmtkisco]

Hi atyy,
Excellent post. Let me look at some of these references and I'll share my thoughts.

Jon

 

[jonmtkisco]

Hi atyy,
I've looked through the references you cited. I have to say that my comprehension of the Grishchuck et al paper is very limited.

I think most of these references are trying to convince the reader that it makes more sense to assume that the background geometry has been warped by gravity than to assume that multiple rulers applied in various different locations and directions have changed size. There is no doubt that the simple mathematical elegance of the spacetime concept is compelling. This explains why it is widely adopted by mainstream GR.

But, in my opinion a MORE IMPORTANT question to ask is: Is it possible to apply SR, on a principled basis, to a collection of individual local reference frames immersed in a cosmic gravitational background, so as to calculate that indeed the rulers which tell us that space is curved are themselves actually lengthend or shortened by Lorentz contraction and dilation? I submit that the integration of Lorentz transformations over an infinitude of adjacent local SR reference frames can explain that the supposed curvature of space is in fact merely a manifestation of lengthened and shortened rulers.

The physical interpretation of specific components of the Einstein Field Equations is well understood to be at best ambiguous and at worst downright murky. The question I'm raising here is what physical interpretation should be given to the precise mathematical results calculated by GR. I do not disagree with the latter at all.

Jon

 

[fakrudeen]

Yes - "matter tells spacetime how to curve, which in turn tells the matter how to move" looks like a round about way saying "matter tells matter how to move" - I can understand where you are coming from.

But I think spacetime curvature is as real as spacetime itself. How physical is spacetime?
Space and time seperately are certainly not physical, because they are "in the eye of beholder".
time as something standing seperately from space broke down with loss of "concept of simultaneouty".
in fact we can measure [and do measure] both in same units [through speed of light].
there is no meaning in saying space is curved - there is no consistent way to separate space from time [that is assign an one and same coordinate-frame] across the whole of spacetime [that is the whole point of GR]!
Only spacetime is real and to the extent it is real, for me curvature is real - which just means extremal "distance" [which is actually proper time in case of spacetime] from A to B is not necessarily euclidean straight line. For example, on Earth's [which is not space but matter] surface I do believe shortest distance is through great circle.
In a sense from the point of probability it would more surprising for spacetime to be flat than curved, because there are more ways to be curved that flat.
Just like we would be surprised if the Earth orbit were to be an exact circle, compared to so many ways for an ellipse to deviate from a circle.

Also how real is quantum states? Al we can get from them as something physical is their "length" as probability of something occurring. Is it just a mathematical tool?

 

[Fra]

Philosophical reflection

I hope this philosophical reflection is not inappropriate here. It seems this thread is firing philosophical question at GR in a way so I might as well throw in my info-perspective here.

John Wheeler famously said: "matter tells Spacetime how to curve, and Spacetime tells matter how to move."

Not to speak for the Wheeler or the correct historical reasoning but my association to this kind of expression is that it's a beautiful statement of an induction principle.

Ie. Matter tells matter how to move, is basically to suggest that matter mysteriously contains the information for it's own differential changes. This has the exact form of an induction, except for it's deterministic tone (which I don't like).

If I may boldly suggest an even better philosophical phrasing that might be more compatible with the quantum indeterminism then one might say that

The matter/energy distribution suggests, by some logic(EinsteinsEquations), how the same is likely to change, give no other a priori reason.

So, what's the meaning of the matter/energy distribution having it's own opinon on it's own change?

The most plausible association I make here is that of uncertainty. If we consider the matter/energy distribution as the information at hand, and that information is generally uncertain, then this contains a self-judgement, where one may expect that the less confident parts are more likely to change than the more confident parts. Here is a seed to the concept of relative inertia. IE. the changes expected to take place, are relational to the current state.

So perhaps we can

- associate the stress energy tensor to information.

- associate the geometry of spacetime as the expectation on the differetial change thereof, induced from the information. This can also be thought of as a self-relating measure, of changes. The state of information, contains a "natural measure" of self-rating, if it's own state.

- the test-particle scenario can be interpreted as a small perturbative change, which is small enough to not distort the measure. The geodesics are the expectations, induced from the current state of information. The evolution of the geodesics are the expected changes of the measures itself.

I think the major lesson from GR is that it contains an element of self-reference, that is the key to the inductive evolution implicit in Einsteins equations. This is philosophically extremely appealing. This is lacking in QM.

So the last thing... what of all this is physical? To me, physical, means more like "physical evidence". Actual data, read by a real observer who is facing real decision problems. To ponder what is real, and not imagine how it's ever going to be established is not sensible to me - it does not answer to real problems. That's more sign of realism ideals.

Real problem for me, are making decisions on incomplete information among other things. It's from this perspective I choose to see GR like the above. It's purpose is to take a grip on GR, that is consistent with a scientific ideal. That IMO originates from limited observations. And this is why the inductive essence of GR is so extremely fascinating. Yet it seems no one has yet unravelled it to it's full beauty (beyond calculational tool).

I hope that one day we will learn to formalize this deeper.

/Fredrik

 

[jonmtkisco]

Hi Fredrik & Fakrudeen,

I want to reiterate that I have no problem with GR's mathematical predictions, I think they give a very accurate mathematical model for whatever the underlying physical process is.

My inquiry in this thread is about trying to not believe in any particular physical theory for gravity, on the grounds that the available data and logic fall far short of what is needed to draw defensible conclusions. I'm not saying that "gravity as a force" should be the preferred theory, just that it should be taken seriously. I'm fairly indifferent to philosophical approaches to the issue.

The mathematical underpinnings of GR seem overwhelmingly complex to experts and amateurs alike in this field. I'd like to break the problem down one step at a time. For example, can we nail down exactly what the sources of this mathematical complexity are, so that we can focus on the fact that gravity mostly has a very simple action?

I'm fairly well convinced that almost all of the mathematical complexity arises from the simple fact that gravitating mass particles (such as protons, neutrons and electrons) are spherically symmetrical point particles. The spherical symmetry of the resulting microscopic gravitational fields seems to be the sole cause of (1) the inverse-square law, (2) tidal effects, and (3) the complexity of the tensors in the Einstein Field Equations used to calculate geodesics through the field. If gravitating particles would exist naturally in the form of infintesimal self-tiling 2-dimensional planes rather than as point spheres which self-pack into larger spheres, the math to describe gravitational action would be really easy: gravity would be a simple, uniform acceleration field. Instead, we are forced to cram a round peg into a square hole, which motivates us to attribute exotic metaphysical properties to many aspects of our universe, including to emptiness itself.

I submit that the idea of warped spacetime as a physically real phenomenon has gained such widespread traction primarily because most people fundamentally overestimate the complexity of the gravitational action. As they say, when the going gets tough, a picture is worth 1000 words.

Jon