Kip Thorne's take on Gravity

[Bill Ryan]

5 hours ago, swansont said:

However, "The greater the slowing of time, the stronger gravity's pull." is incorrect. Time dilation is dependent on the gravitational potential, not directly on the strength of gravity. Someone inside of a uniform spherical mass shell feels no gravity, but would experience time dilation.

I think this might be the exception that proves the rule because it is not really time dilation that causes gravitational attraction - it's the gradient. In your example time is running slower but the gradient is the same in all directions - so no attraction.  Not true standing on earth getting hit by a falling apple where time dilation changes along the vertical.

[swansont]

4 hours ago, Bill Ryan said:

I think this might be the exception that proves the rule because it is not really time dilation that causes gravitational attraction - it's the gradient. In your example time is running slower but the gradient is the same in all directions - so no attraction.  Not true standing on earth getting hit by a falling apple where time dilation changes along the vertical.

But that's not what the quote said.

[Bill Ryan]

2 hours ago, swansont said:

But that's not what the quote said.

Right - I see that.  There is a possible contextual explanation.  I'm guessing Kip Thorne is talking about the same thing I am going on about it but I don't know yet.

[Bill Ryan]

Here is context for Kip Thorne quote from Chapter 4 of The Science of Interstellar (it includes from page 35 a chapter title and opening paragraph and then the sentence quoted above and then on pp 291-2 a technical note - bold emphasis mine and my annotations in brackets.  The use of italics is Thorne's.  If there are errors, it is my transcription.):

Chapter 4

Warped Time and Space, and Tidal Gravity

Einstein's Law of Time Warps  [For those of you hoping that Thorne "comes to his senses" - by your lights - the fact that he has plopped this pithy moniker on what follows augurs badly.]

Einstein struggled to understand gravity on and off from 1907 onward.  Finally in 1912 he had a brilliant inspiration.  Time , he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity.  He embodied this insight in what I like to call "Einstein's law of time warps," a precise mathematical formula¹  that I describe qualitatively this way: Everything likes to live where it will age the most slowly, and gravity pulls it there.

The greater the slowing of time, the stronger gravity's pull.  On Earth, ...

[And here is the referenced technical note]

The simplest, quantitative form of Einstein's law of time warps is this: Place two identical clocks near each other, and at rest with respect to each other, separated from each other along the direction of the gravitational pull that they feel. Denote by R the fractional difference in their ticking rates, by D the distance between them, and by g the acceleration of the gravity they feel (which points from the one that ages the fastest to the one that ages the slowest).  Then Einstein's law says that g=Rc² /D. For the Pound-Rebca experiment in the Harvard tower, R was 210 picoseconds in one day, which is 2.43 X 10^-15 , and the tower height D was 73 feet (22.3 meters).  Inserting these into Einstein's law, we deduce g= 9.8 meters/second² , which indeed is the gravitational acceleration on Earth.

[Admittedly, I did not check his math.]

[geordief]

There is more from Kip Thorne  here

https://www.its.caltech.edu/~kip/scripts/PubScans/BlackHoles-Thorne-Starmus.pdf

 

"Now, Einstein’s Law of Time Warps says that “Things like to live where they age the most slowly, and gravity pulls them there”. On Earth, time flows more slowly than in outer space by 4 parts in 10 billion, and that (according to Einstein) is enough to account for the gravity that holds us on the Earth’s surface. Since the slowing of time becomes enormous as one nears a black hole’s horizon, the pull of gravity becomes enormous there; and precisely at the horizon, time slows to a complete halt, so the pull of gravity is infinite. Inside the horizon, time still flows – but, strangely, it flows in a direction that you would have thought is spatial: toward the singularity at the hole’s center. This is why nothing can get out of a black hole; to get out, things would have to travel upward, which means backward in time, and nothing can do that. This explanation of a black hole’s blackness is equivalent to the “infinite gravitational pull” explanation. The two explanations are related by Einstein’s Law of Time Warps."

 

I can't comment .

[swansont]

10 hours ago, Bill Ryan said:

Here is context for Kip Thorne quote from Chapter 4 of The Science of Interstellar (it includes from page 35 a chapter title and opening paragraph and then the sentence quoted above and then on pp 291-2 a technical note - bold emphasis mine and my annotations in brackets.  The use of italics is Thorne's.  If there are errors, it is my transcription.):

Chapter 4

Warped Time and Space, and Tidal Gravity

Einstein's Law of Time Warps  [For those of you hoping that Thorne "comes to his senses" - by your lights - the fact that he has plopped this pithy moniker on what follows augurs badly.]

Einstein struggled to understand gravity on and off from 1907 onward.  Finally in 1912 he had a brilliant inspiration.  Time , he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity.  He embodied this insight in what I like to call "Einstein's law of time warps," a precise mathematical formula¹  that I describe qualitatively this way: Everything likes to live where it will age the most slowly, and gravity pulls it there.

The greater the slowing of time, the stronger gravity's pull.  On Earth, ...

[And here is the referenced technical note]

The simplest, quantitative form of Einstein's law of time warps is this: Place two identical clocks near each other, and at rest with respect to each other, separated from each other along the direction of the gravitational pull that they feel. Denote by R the fractional difference in their ticking rates, by D the distance between them, and by g the acceleration of the gravity they feel (which points from the one that ages the fastest to the one that ages the slowest).  Then Einstein's law says that g=Rc² /D. For the Pound-Rebca experiment in the Harvard tower, R was 210 picoseconds in one day, which is 2.43 X 10^-15 , and the tower height D was 73 feet (22.3 meters).  Inserting these into Einstein's law, we deduce g= 9.8 meters/second² , which indeed is the gravitational acceleration on Earth.

[Admittedly, I did not check his math.]

IOW, R = gh/c^2 (in regions where you can assume g is constant) which is a well-known time dilation formula

As I said, all one has done is rewrite the equations.

However, it is a conceptual leap to say that time dilation causes gravity. We also experience time dilation from relative motion, and one would have to show that that causes gravitational effects, or explain why it should not. Satellites experience kinematic time dilation that is comparable to the gravitational effects, and their orbits are consistent with the expected Newtonian ones, so we can safely conclude that time dilation does not cause gravitational accelerations.

 

[Bill Ryan]

Time dilation does not cause gravity.   But in a gravitational field, time dilation changes along the radius.  And that change in value according to location (the gradient) causes gravitational attraction. I think the Thorne quote above justifies this interpretation. "Warp" here means curvature. Otherwise, the whimsical "everything likes to live where it will age the most slowly," wouldn't really apply.  How would things get to live there if all available aging were at the same rate?   Thorne's formula takes the data points of the gradient, not the slow rate as such.  I think when he says"The greater the slowing of time, the stronger gravity's pull," this is true because stronger fields means steeper gradients (I would think generally at least.)

So for your first counterexample, the formula works.  Outside of a gravitational field, in my fast spaceship, I have two clocks.  They may be slow with respect to the outside world but there is no "fractional difference in their ticking rates" between them: R= zero , g = 0c²/D = 0. 

I have now reached or surpassed my math ability so I can't use math in your second example.  Maybe the answer above is worth something because your second counterexample is, as I understand it, also about special relativity.   

 

[Bill Ryan]

Several people on this thread have questioned Kip Thorne’s language by pointing out that space and time are not separate. True – but they are nevertheless distinguishable.  As Thorne says, Einstein’s 1911 attempt to describe the effect of gravitation on light takes only time curvature into account.  It produces a bending prediction that is off by half. When he later gets his math act together and models spacetime he subsumes the earlier model. He does not dump it.  He complements time curvature with space curvature and nails the prediction.

Also, in non-extreme gravity, such as Earth’s, and at non-relativistic speeds, space is essentially flat and the entirety of mass’s effect on motion (gravitational attraction) can be understood as the result of time curvature.  The falling apple (and even the orbiting Earth) are simply not moving much in the space component of spacetime.  (Time is made equivalent to space by the speed of light so as we sit here reading this in a chair or in an airplane or while skydiving, our progress through space is de minimis. But we and the apple are all going very fast – through time.)  Under these conditions, with respect to motion, time dominates and GR reduces to Newton.

Some others on the thread seem to believe that there is a critique of GR lurking here.  All of the above is in support of GR and its author.   It has been repeatedly described in its essentials by Einstein and many others since.  As far as I can tell, it may appear exotic or even egregious because of a widespread pedagogical failure, but it is definitely part of GR.

Here are some Einstein sources and excerpts that I think support the Kip Thorne case (quotes mark excerpts.  My comments inside excerpts are in brackets):

1911

In 1911 Einstein published On the Influence of Gravitation on the Propagation of Light. He explains that light’s behavior in a gravitational field demonstrates that time flows slower near the gravitational source.  The marker for this is an apparent variation in the speed of light.  The show-stopper comes in the middle of page 107 as this is reprinted in the Dover paperback The Principle of Relativity. 

“From the proposition which has just been proved, that the velocity of light in the gravitational field is a function of the place, we may easily infer, by means of Huyghens’s principle, that light rays propagated across a gravitational field undergo deflexion.”

This is followed by a little diagram showing the plane light-wave changing direction as a result of crossing a time gradient.  This is equivalent to optical refraction where varying thickness of a retarding medium alters the path of light (which is why he has dragged in Huyghens.)

Think of the wave as a group of ice skaters in chorus line formation, shoulder to shoulder and arms locked, all skating with equal effort.  As you move from right to left on the line (as they are facing) the ice is increasingly slushy (they are skating across a temperature gradient), the slush retards each skater to a different degree and the line inexorably turns left. Time moves more slowly as you get closer to the surface of the sun.  So the equivalent of turning left is to bend toward the sun – otherwise known as falling.

Why are we watching the sausage being made?  If the 1911 theory were thrown out in 1915 then this discussion might be a sterile curiosity.  But that did not happen.  It is absorbed into general relativity as the Newton limit. It was not a complete description of bending light because light is covering as much space as it is time so space curvature and time curvature play equivalent and reinforcing roles and Einstein had not yet gotten a grip on curved space. But re-contextualized, as a component of spacetime, time curvature remains an accurate explanation and predictor for the dropping apple.

1915

In The General Theory of Relativity section of The Meaning of Relativity – Fifth Edition MJF Books - Einstein presents the general relativity equation on page 79 for the “motion of a material particle, under the action only of inertia and gravitation” and then asks on page 80, “How are these [GR] equations connected with Newton’s equations of motion?” On page 81 he answers “Let the velocity of the material particles be very small compared to that of light…dx₁/ds , dx₂/ds, dx₃/ds [the curvature components of the three spatial dimensions] will vanish compared to dx₄/ds [time curvature]…This [resulting] equation is identical with Newton’s equation of motion for a material particle in a gravitational field…”

In The Foundation of the General Theory of Relativity in a section titled Newton’s Theory as a First Approximation Einstein goes through a similar exercise and states on page 158,9 of The Principle of Relativity, “If we restrict ourselves to the case which almost exclusively offers itself to our experience, of v being small as compared with the velocity of light…What is remarkable in this result is that the component g₄₄ [the time component pf spacetime curvature (in modern notation: g₀₀)] of the fundamental tensor alone defines, to a first approximation, the motion of a material point.”

My final piece of evidence is in Relativity The Special and General Theory, which he wrote (in contrast with the above sources) for mere civilians such as myself. In Appendix III The Experimental Confirmation of the General Theory of Relativity, he lays out on page 127 of the Crown Publishers paperback the confirmed angle of deflection of starlight around the sun and then, “It may be added that, according to the theory, half of this deflection is produced by the Newtonian field of attraction of the sun, and the other half by the geometrical modification (“curvature”) of space caused by the sun.”

This unfortunate formulation (apparently in service of keeping it simple) gives the impression that GR might be something pasted on to Newton instead of subsuming it. It also gives the impression that geometrical considerations only apply to space as opposed to spacetime. It is only from the standpoint of the actual theory as indicated by the previous references that we can recapitulate Einstein by substituting “time curvature” for “Newtonian field of attraction.”  I think this pedagogical misstep, and related ones since, are at the heart of the confusion about Kip Thorne’s idea.  See this Physics Forum link for the trouble caused by the Einstein quote.

https://www.physicsforums.com/threads/a-baffling-quote-from-einstein-badly-requiring-explanation.300849/

 

Edited July 8, 2018 by Bill Ryan

[Markus Hanke]

Since the g{tt} component of the metric tensor contains the factor c, and hence “dominates” the metric in a certain sense, it is not a surprise that it makes a large contribution to the overall geodesic deviation, at least under some circumstances. And the bit in bold is the key, because the relationships between the metric tensor components in the field equations are of a highly non-linear nature. This non-linearity is small in the weak-field vacuum regime (such as the Earth), but becomes increasingly noticeable in strong field regimes. It also becomes noticeable when the spacetime in question is not stationary, and in particular when you go from vacuum to the interior of energy-momentum distributions. Under such circumstances, tidal forces (which mostly arise from the spatial part of the metric, instead of the temporal one) play as much, or even more, of a role than gravitational time dilation.

In my humble opinion it makes no sense at all to attempt to separate these effects, except perhaps as pedagogical aids, or as approximations in special cases to simplify the maths. Other than that, spacetime is the gravitational field - you can’t meaningfully separate them. And why would you want to? It is precisely that identification of spacetime with the gravitational field, which makes GR so powerful.

[Bill Ryan]

On 7/9/2018 at 1:27 AM, Markus Hanke said:

In my humble opinion it makes no sense at all to attempt to separate these effects, except perhaps as pedagogical aids, or as approximations in special cases to simplify the maths.

Kip Thorne is not making this point to simplify the maths. To predict motion in the circumstances under discussion without wearing down a pencil just skip GR altogether. Thorne is pursuing this to illuminate the physics.

 As to pedagogy, sure, but I have a hard time untanglling that from an actual physics dispute.  Bad pedagogy certainly contributes to the persistence of the disagreement.  Every GR course addresses the Newtonian limit, but apparently many (not all) skip over what this physically means (time curvature cause of attraction) and quickly move to GR verification in clock discrepancies.  Herbert Hamber's recorded course does describe it directly, but briefly.  

 John Wheeler’s GR distillation applies to time here. “Matter tells space how to curve and space tells matter how to move.”  (Let’s admit “space” is short for “spacetime.”) In the circumstances under discussion, the everyday experience of gravity on Earth (outside the source, low velocity, moderate field),  Wheeler can be reasonably recapitulated as “Matter tells time how to curve and curved time tells matter how to move.” 

 Curved time means a time rate gradient along the z axis. Passage through time is across this gradient and results in a deviation analogous to refraction which we call falling. This is spacetime curvature in this instance. The time component is no less geometric than the space component and it is the only significant  component under these limited circumstances. 

 How often do you read that gravity causes clocks to vary in speed according to height?  This is a miserable formulation which buries Wheeler’s simple causal sequence in a sloppy anti-GR inversion. It’s as if there is a Newtonian force of attraction and the closer you are to its source the slower time goes. No. As we know, there is only mass shaping the metric field (in this case, varying rates of time flow) which in turn directs motion. 

 Not only can the idea of spacetime withstand analysis – it is enhanced by looking at how its parts work. I understand the Einstein equation adds up to a universal picture true for all reference frames but Thorne is simply doing with words what Gμν does by pairing all the dimensions. The equation is an analytic as well as synthetic machine. I don’t think you advance GR by deploying “spacetime” as a gloss to resist Thorne’s physical intuition about time.

[Markus Hanke]

3 hours ago, Bill Ryan said:

In the circumstances under discussion, the everyday experience of gravity on Earth

Yes, that is one of the special cases I mentioned.

3 hours ago, Bill Ryan said:

As we know, there is only mass shaping the metric field

Again, this is true only for special cases (such as Schwarzschild-type metrics)

3 hours ago, Bill Ryan said:

in this case, varying rates of time flow

There is not really any such thing as a “rate of time flow”. Time dilation is not something that happens locally, it is a relationship between clocks in spacetime. Locally, all clocks always tick at “1 second per second” - it is only when you compare two or more clocks in spacetime that you can meaningfully speak of time dilation.

[geordief]

1 hour ago, Markus Hanke said:

Yes, that is one of the special cases I mentioned.

Again, this is true only for special cases (such as Schwarzschild-type metrics)

There is not really any such thing as a “rate of time flow”. Time dilation is not something that happens locally, it is a relationship between clocks in spacetime. Locally, all clocks always tick at “1 second per second” - it is only when you compare two or more clocks in spacetime that you can meaningfully speak of time dilation.

Can  time be seen as  a property of something rather than a thing in its own right?

 

If so,  must there always be a  something for time to be a property of ** and can  this something always be described as a system of some sort?

Would radioactive decay  be described as a system ?

 

 

[swansont]

8 hours ago, Bill Ryan said:

  John Wheeler’s GR distillation applies to time here. “Matter tells space how to curve and space tells matter how to move.”  (Let’s admit “space” is short for “spacetime.”) In the circumstances under discussion, the everyday experience of gravity on Earth (outside the source, low velocity, moderate field),  Wheeler can be reasonably recapitulated as “Matter tells time how to curve and curved time tells matter how to move.” 

Curved time doesn't make a whole lot of sense. It's a scalar. How does it curve?

8 hours ago, Bill Ryan said:

 Curved time means a time rate gradient along the z axis.

You've invoked a spatial dimension here.

8 hours ago, Bill Ryan said:

Passage through time is across this gradient and results in a deviation analogous to refraction which we call falling. This is spacetime curvature in this instance. The time component is no less geometric than the space component and it is the only significant  component under these limited circumstances. 

 How often do you read that gravity causes clocks to vary in speed according to height?  This is a miserable formulation which buries Wheeler’s simple causal sequence in a sloppy anti-GR inversion. It’s as if there is a Newtonian force of attraction and the closer you are to its source the slower time goes. No. As we know, there is only mass shaping the metric field (in this case, varying rates of time flow) which in turn directs motion. 

Except that we know it's not the value of g, but the gravitational potential that is the important quantity.

 

[Markus Hanke]

2 hours ago, geordief said:

Can  time be seen as  a property of something rather than a thing in its own right?

Not in mainstream physics, no.

However, there are speculations and hypotheses - mostly in the realm of metaphysics and philosophy - which consider the question of whether our sensed “flow of time” is an artefact of our perception/brain, rather than a fundamental part of nature. I don’t think this type of speculation belongs into this thread, though.

7 minutes ago, swansont said:

Except that we know it's not the value of g, but the gravitational potential that is the important quantity.

This is true, but there is a caveat - the notion of “gravitational potential” can only be meaningfully defined in spacetimes that admit a time-like Killing field, whereas time dilation arises directly from the metric. So I would argue that time dilation is a more general concept than gravitational potential.

But of course, in Schwarzschild spacetime the two concepts are largely interchangeable, due to the symmetries present here.

[Bill Ryan]

On 8/6/2018 at 2:48 AM, geordief said:

There is not really any such thing as a “rate of time flow”. Time dilation is not something that happens locally, it is a relationship between clocks in spacetime. Locally, all clocks always tick at “1 second per second” - it is only when you compare two or more clocks in spacetime that you can meaningfully speak of time dilation.

Sorry for the crumby wording - what you said is what I was referring to (and have illustrated in several posts in this thread.) 

[Bill Ryan]

On 8/6/2018 at 5:29 AM, swansont said:

On 8/5/2018 at 9:07 PM, Bill Ryan said:

  John Wheeler’s GR distillation applies to time here. “Matter tells space how to curve and space tells matter how to move.”  (Let’s admit “space” is short for “spacetime.”) In the circumstances under discussion, the everyday experience of gravity on Earth (outside the source, low velocity, moderate field),  Wheeler can be reasonably recapitulated as “Matter tells time how to curve and curved time tells matter how to move.” 

Curved time doesn't make a whole lot of sense. It's a scalar. How does it curve?

Responding in two parts:

1.) Regarding the "scalar" point - good question.  Are x, y and z scalars? In any case if you are arguing that the space components of space-time may be curved but time is just along for the ride, I think that's a problem.  Maybe it's THE problem. Space-time in its totality and its parts is geometry. 

2.) With respect to "how does it curve?" we are ships passing in the night.  My last several posts comprise a description of its curvature and the mechanism by which this results in the totality of gravitational attraction in every day circumstances. The marker for its curvature is time dilation along the z axis. The mechanism by which passage across the time gradient results in "attraction" is equivalent to refraction.

Let me now say it in a different way and you tell me what is wrong with this. Imagine normalizing time by converting it into a synthetic negative space dimension - multiplying by -c. As a result we now have "the world" - a four dimensional geometry warped by the presence of mass (among other things).  And in this world the time gradient has been remodeled as a spatial distortion equivalent to the spatial distortion in the space dimensions. Applying parallel transport to geodesics we document curvature - all four dimensions contributing. (Except with the dropping apple viewed from a nearby picnic only one dimension's curvature shows up - that of time.)  

One might argue that this normalization of time is a trick in modeling,  that it has questionable ontological standing and results in unfortunate artifacts, but most of us prefer to see Einstein and his contemporaries as heroically accomplishing Ahab's mission and  "striking through the mask" thereby grasping a world more real than the phenomenal.  In any case, this is the model.  It is geometrical - all four dimensions.  On July 8th above I quoted Einstein veering from this perspective (the quote repeated below). I think where you stand with respect to this quote goes to the heart of our dispute. In my estimation this is not the master at his best.  

On 7/8/2018 at 3:59 PM, Bill Ryan said:

[quoting Einstein] "...It may be added that, according to the theory, half of this deflection is produced by the Newtonian field of attraction of the sun, and the other half by the geometrical modification (“curvature”) of space caused by the sun.”

 

On 8/6/2018 at 5:29 AM, swansont said:

Quote

 Curved time means a time rate gradient along the z axis.

You've invoked a spatial dimension here

I have indeed.  But if you are implying that I am therefore admitting that space curvature is a component of the cause of attraction in these limited circumstances - I am not.  It's all time all day long.  The significance of z here is entirely as to the disposition of the time gradient and therefore the direction of "attraction."  I am essentially restating Einstein's 1911 argument quoted above on July 8th (including the z axis) and he was not offering up spatial curvature at the time.

[Markus Hanke]

Gravity is geodesic deviation - and in the geodesic deviation equation, it is not straightforwardly possible to separate the “time” from the “space” contributions. I don’t think such an approach is very meaningful. What we can do, however, is look at the metric itself, and sometimes (like e.g. in the case of Schwarzschild) we see that the time part plays a bigger role than the space part, due to the presence of a factor of c squared. 

It should be noted though that this is not always true - for example, in the immediate vicinity of a black hole with a very small mass, the spatial contributions would be at least on the same order of magnitude than the time contributions. And then of course you have cases where the metric has non-vanishing off-diagonal terms...

[geordief]

10 hours ago, Bill Ryan said:

Sorry for the crumby wording - what you said is what I was referring to (and have illustrated in several posts in this thread.) 

Not my quote btw. Your cut and paste went awry.**That was Markus' .

**or whatever happened

Edited August 23, 2018 by geordief

[Bill Ryan]

Geordief - I see that - sorry