Cause of Gravity: Lewis Epstein's Theory Explained

[CRichard]

Hi everyone. This is my first post and it's sort of related to homework because it's for a paper I'm writing for school but it's pretty conceptual so I thought I'd put it here.

In Lewis Epstein's book Relativity Visualized, he says that it's actually the slowing of time rather than the curving of space that's the major cause of gravity. He "proves" this by explaining that light is bent by matter and follows an arc. As a result, time has to go slower as you go down deeper into the arc (closer to matter) because that light doesn't have as much distance to cover.

Epstein then gives a visual argument as to why this causes gravity: If you have a spacetime diagram on a piece of paper, slow time close to matter corresponds to a lengthening of one end of the paper, so that the shape is like a piece of pizza (with the wider end being close to matter). Since everything tends to follow straight lines, you can draw a straight line through this piece of paper and take it to represent an object being thrown or just traveling horizontally in space. Epstein's reasoning is then that you can fold this paper into a cone (which is allowed because it doesn't change the nature of spacetime) and then see that the straight line actually curves toward the wider end of the cone. This is how gravity comes about.

My only concern with this theory is that his first point, that bent light causes time to slow, still doesn't explain the actual bending of light. He uses bent light to explain the cause of gravity, but bent light is actually caused by gravity! (I think) Am I right that this explanation isn't right? Also, is his statement true that slow time, rather than warped space, causes the everyday gravity that we experience?

Sorry if this has been answered before. This question has been nagging me, since Epstein's book as a whole is such a great intro to relativity.

 

[zhermes]

This is a really good question---and you're bringing up a really good point.

1) You're right that his argument (or at least your understanding of it) is circular. The "cause" of gravity is a very complicated question. Mass(energy) is what causes the effects of gravity; bending of spacetime is one way of understanding the causes of gravitational effects on massive(energetic) bodies. What the cause is, of gravity existing in the first place---is a question for a philosopher, not a physicist. So be careful with what type of 'cause' is being discussed.

The apparent bending of space-time is the way it works; no one can say why that's the way it is.

2) The curved path of light is evidence of time-dilation. Once you construct a complete description (general relativity), you see that time and space are treated identically. Thus, I believe it's misleading to say that the 'slowing of time' has a larger effect than 'bending of space'---they're really the same thing (or at least two sides of the same coin). It might be better to take what he's saying as: our interpretation of the effects of gravity may be more influenced by the effects on time than the spatial dimensions... in any case, I think its a fairly subjective statement.

Hope that helps.

 

[Bill_K]

Wow. If this is an accurate account of what Epstein says, all I can say is, I'd quickly look for another book on relativity.

 

[CRichard]

@ zhermes: Thanks, that definitely makes a lot of sense that time slowing and warped space are two equivalent contributions to gravity and are two results of mass. For a while I thought that Epstein had shown why gravity needs to exist but now I'll have to settle for the fact that mass produces it and that's the way it is :)

@ Bill K: It's weird because the rest of the book is, I think, very solid. He tries to show how relativity works with diagrams and intuitive explanations rather than math or explicit detail. I could have misinterpreted this point, but I'm pretty sure that's what he was getting at.

 

[TobyC]

I don't know an awful lot about general relativity but you might be interested in this sentence from a book I'm reading (A first course in General Relativity by Bernard Schutz) which I think is quite a respected book.

'Newtonian gravity is produced exclusively by the curvature of time in spacetime, spatial curvature comes in only at the level of post-Newtonian corrections'

Intuitively this seems to make sense, the space that we're familiar with is pretty much flat, it follows euclidean geometry, that's why euclid came up with it 2000 years ago. Yet we are still able to feel the effects of gravity, so if gravity is caused by curvature then it should be curvature of time rather than of space.

 

[slcoleman]

Food for thought, because this is one of my favourite topics. ;)

By all current theories, Gravity is caused by a curvature in space time. In essence they are invoking 'geometry' (physical representation) to explain a 'force' (energy). By this theory things move by geodesics through this euclidean space, and this seems plausible, but then there is still a problem. If an object is stationary in space what supplies the energy for that object to accelerate in the first place? Geometry does not 'supply' energy. Even time does not 'supply' energy. So clearly there is still a part of the system that has not been explained by our current theory(s). The lack of usable/convertible energy in the GR theory is the 'elephant in the room' that no one is talking about. It can't be explained away by either geometry or time warping alone.

We know that Energy can not be created, and the object being accelerated is definitely not getting smaller so its not coming from the mass itself. The space and time doesn't appear to change until you accelerate fast enough. Even then the mass/energy grows as the square of its speed, so where did all that energy and excess mass come from? If it comes from somewhere, then what changed in that location after giving up that energy? There is no free ride even in QM or relativity.

 

[Dale]

If an object is stationary in space what supplies the energy for that object to accelerate in the first place? Geometry does not 'supply' energy. Even time does not 'supply' energy. So clearly there is still a part of the system that has not been explained by our current theory(s). The lack of usable/convertible energy in the GR theory is the 'elephant in the room' that no one is talking about. It can't be explained away by either geometry or time warping alone.

You need to study a little more before making this kind of absurd statement. This is completely well-explained and consistent in the theory and is not an "elephant in the room that no one is talking about". In fact, there have been many threads on this forum which have addressed exactly this question.

The key point is that it is not space that is curved but spacetime. Even if a particle is "at rest" it still "moves" along the time dimension.

 

[Passionflower]

The key point is that it is not space that is curved but spacetime. Even if a particle is "at rest" it still "moves" along the time dimension.

There are solutions (for instance the internal Schwarzschild solution) though where at some locations a particle's time is 'at rest' as a matter of speaking. However those solutions may not be physical.

 

[slcoleman]

You need to study a little more before making this kind of absurd statement. This is completely well-explained and consistent in the theory and is not an "elephant in the room that no one is talking about". In fact, there have been many threads on this forum which have addressed exactly this question.

The key point is that it is not space that is curved but spacetime. Even if a particle is "at rest" it still "moves" along the time dimension.

@DaleSpam: I certainly do not want to come off disrespectful, but why is the requirement for energy conservation considered by you to be an absurd statement? I have read every GR book I could get my hands on and nowhere, except one bizarre reference I can't remember the off of the top of my head, even mentioned the requirement of energy conservation for GM particle acceleration. The one that did gave no solution and posed it as a problem that is still unsolved. If you have any specific references (this forum or otherwise) to where this required energy exchange comes from I would sincerely appreciate a pointer to it. A formula showing that all energy is strictly conserved and that can be plugged into Mathematica to simulate a simple free fall through space time would be great.

 

[Dale]

The absurd statements were the ones claiming that the acceleration of an object initially at rest is a topic which has not been investigated, or which geometry and GR cannot explain (e.g. "elephant in the room"). That is completely absurd.

In GR local energy and momentum conservation are enforced by the continuity of the stress-energy tensor, which can be derived from the EFE. Energy is not generally conserved globally in GR for arbitrary spacetimes, but that is unrelated to the fact that an object at rest can accelerate.

The fact that objects initially at rest accelerate is simply due to the fact that it is spacetime which is curved and not just space. Loosely speaking, some of the "movement through time" curves into "movement through space". This acceleration of initially parallel geodesic worldlines is precisely what it means for spacetime to be curved.

 

[khemist]

@DaleSpam: I certainly do not want to come off disrespectful, but why is the requirement for energy conservation considered by you to be an absurd statement? I have read every GR book I could get my hands on and nowhere, except one bizarre reference I can't remember the off of the top of my head, even mentioned the requirement of energy conservation for GM particle acceleration. The one that did gave no solution and posed it as a problem that is still unsolved. If you have any specific references (this forum or otherwise) to where this required energy exchange comes from I would sincerely appreciate a pointer to it. A formula showing that all energy is strictly conserved and that can be plugged into Mathematica to simulate a simple free fall through space time would be great.

The energy comes from the gravitational field, in the form of potential gravitational energy. It is similar to the potential created in an electric field, known as a voltage.

Correct me if I am wrong, but a simple freefall in space would be simply F = ma, where F is the gravitational force and a is the gravitational acceleration. In the case of earth, it is F = mg, where g = 9.8 m/s^2.

 

[slcoleman]

@DaleSpam: I guess we will have to agree to disagree on the applicability of the word absurd. The topic of the discussion here was on the 'Cause or Gravity' and I was merely trying to get people to look at something from a slightly different perspective rather than asking them to ponder a question point blank that people generally just throw up their hands at rather than thinking for themselves. From an advanced philosophical perspective thinking differently is more likely to find a new solution. It seems to me that thought experiments have been useful in the past.

Ok, the point blank question is 'what is G derived from'? We both know that the G in the EFE is what is distributed within the stress energy tensor that works its magic to such a high degree of accuracy here on Earth (pioneer, dark matter, and dark energy can be left to another discussion). The 'constant' G was painstakingly obtained by applying statistical analysis to observations to many many experimental tests, and is therefore quite successful in predicting most of the phenomenon that we observe. The problem is that G is not defined by any set of processes or interactions that can be used to describe why G has its specific value that it does. We take it for granted as an energy source (over simplification I know) and we just plug it into whatever formula of our choosing without giving it a second thought. Its mathematically convenient.

String, M theory, and particle physicists are all attempting to explain the source of G via unification to electromagnetism, weak, strong, etc, but so far the jury is still out on all accounts. Until you know what causes the exact value of G through the summation of all participating attributes/processes/interactions you have not yet created a complete theory of Gravity. When you do have a truly complete GR theory you will also by extension have complete energy conservation expressed in each and every formula that deals with gravitation. Until then we will never be able to account for the missing energy that G represents. G is a place holder simply because we don't know enough about it to be able to do otherwise.

 

[Dale]

Ok, the point blank question is 'what is G derived from'? ... The problem is that G is not defined by any set of processes or interactions that can be used to describe why G has its specific value that it does.

G has the specific value that it does simply because of our choice of units. We can give G any value we wish simply by choosing different units. The same is true for all dimensionful constants. It is only the dimensionless constants that have any physical meaning beyond our choice of units.

Also, the non-conservation of energy in GR has nothing to do with the value of G. Nor does it have anything to do with your original point about objects accelerating from rest.

 

[yogi]

G has the specific value that it does simply because of our choice of units. We can give G any value we wish simply by choosing different units. The same is true for all dimensionful constants. It is only the dimensionless constants that have any physical meaning beyond our choice of units.

That is not true - G has a value in relation to the other units we pick - meters or yards would result in a different numerical value - ntn vs pounds would be another variable ...but G always has a unique relational functionality with respect to the other dimensions in which the variables are expressed

Einstein made a number of assumptions - that space was closed and the universe was static - both wrong as far as we know today - but he had great insight, and with no physics available he devised a solution - just as he had done in special relativity he turned the probelem into a postulate - curved space and slow time worked - but there was not then, nor is there now an understanding of how inert matter can affect static space - we don't know what space is - and therefore have no physics to explain the curvature - nor do we have a generally accepted theory as to what causes G to have the value we measure - Einstein didn't have a postulate fix for the value of G

 

[yogi]

@DaleSpam: I guess we will have to agree to disagree on the applicability of the word absurd. The topic of the discussion here was on the 'Cause or Gravity' and I was merely trying to get people to look at something from a slightly different perspective rather than asking them to ponder a question point blank that people generally just throw up their hands at rather than thinking for themselves. From an advanced philosophical perspective thinking differently is more likely to find a new solution. It seems to me that thought experiments have been useful in the past.

Ok, the point blank question is 'what is G derived from'? We both know that the G in the EFE is what is distributed within the stress energy tensor that works its magic to such a high degree of accuracy here on Earth (pioneer, dark matter, and dark energy can be left to another discussion). The 'constant' G was painstakingly obtained by applying statistical analysis to observations to many many experimental tests, and is therefore quite successful in predicting most of the phenomenon that we observe. The problem is that G is not defined by any set of processes or interactions that can be used to describe why G has its specific value that it does. We take it for granted as an energy source (over simplification I know) and we just plug it into whatever formula of our choosing without giving it a second thought. Its mathematically convenient.

String, M theory, and particle physicists are all attempting to explain the source of G via unification to electromagnetism, weak, strong, etc, but so far the jury is still out on all accounts. Until you know what causes the exact value of G through the summation of all participating attributes/processes/interactions you have not yet created a complete theory of Gravity. When you do have a truly complete GR theory you will also by extension have complete energy conservation expressed in each and every formula that deals with gravitation. Until then we will never be able to account for the missing energy that G represents. G is a place holder simply because we don't know enough about it to be able to do otherwise.

I think those are excellent observations - but the answer for why G has the value we measure may lie in classical physics rather than quantum theory - a number that is quite close can be derived from the present Hubble acceleration rate c^2/R i.e.,
G= [c^2/4(pi)R][m^2/kgm]

 

[Dale]

the answer for why G has the value we measure may lie in classical physics rather than quantum theory - a number that is quite close can be derived from the present Hubble acceleration rate c^2/R i.e.,
G= [c^2/4(pi)R][m^2/kgm]

That is numerology, not science.

 

[Dale]

we don't know what space is - and therefore have no physics to explain the curvature

Yes, we do: the EFE does exactly that.

nor do we have a generally accepted theory as to what causes G to have the value we measure

We know exactly what causes that: our choice of units. The values of all the dimensionful fundamental constants (c, G, h, etc.) are artifacts of our choice of units and can have any value completely dependent on our choice of units. The dimensionless constants (fine structure constant, gravitational coupling constant, etc.) are the ones that have a physical meaning beyond our choice of units. See:
http://math.ucr.edu/home/baez/constants.html

Furthermore, if you alter the dimensionful constants such that the dimensionless constants are unchanged then you wind up with no measureable physical change. On the other hand, if you change the dimensionless constants then the change is physically measurable.
https://www.physicsforums.com/showpost.php?p=2011753&postcount=55
https://www.physicsforums.com/showpost.php?p=2015734&postcount=68

 

[yogi]

Yes, we do: the EFE does exactly that.

We know exactly what causes that: our choice of units. The values of all the dimensionful fundamental constants (c, G, h, etc.) are artifacts of our choice of units and can have any value completely dependent on our choice of units. The dimensionless constants (fine structure constant, gravitational coupling constant, etc.) are the ones that have a physical meaning beyond our choice of units. See:
http://math.ucr.edu/home/baez/constants.html

Your missing the whole point - whatever units we use to express G - it will always measure the same - G appears to be temporally constant irrespective of the dimensions we use - but the units are significant - they show the fundamental tie between the physical thing (i.e., the law of Gravity) and its relationship to the cause that brings about the multiplying factor needed to make experimental measurements conform to the underlying theory. In the case of G, the units are cubic meters per sec squared per kgm - i.e., volumetric acceleration/kgm. And the volumetric acceleration of the universe within the limits of experimental error comports with the experimentally determined value of G - that is not numerology - it comes directly from Freidmann's equation.

 

[yogi]

"Yes, we do: the EFE does exactly that."

Wrong again. In the Einstein Field equations, the value of G is put in by hand - the General theory does not answer why G has a particular value ... the General Theory is incomplete in this regard.

 

[Dale]

"Yes, we do: the EFE does exactly that."

Wrong again. In the Einstein Field equations, the value of G is put in by hand

So what? Even if the value of G is put in by hand the EFE still explains the curvature: it comes from the stress-energy distribution.

 

[Dale]

G appears to be temporally constant irrespective of the dimensions we use - the units are significant - they show the fundamental tie between the physical thing (i.e., the law of Gravity) and its relationship to the cause that brings about the multiplying factor needed to make experimental measurements conform to the underlying theory.

No, they don't. All they do is show the relationship between the different units we are using. Please read the links I provided above. The constants that describe actual physics are necessarily dimensionless. In this case, you are probably thinking of the gravitational coupling constant.

 

[slcoleman]

the EFE still explains the curvature

Just a slight correction for accuracy, the EFE allows us to calculate the effects of the curvature. Nothing in the EFE explains why there is a curvature. If we knew why there is a curvature we would have energy conservation, unification with the other forces, and a complete theory. Saying that mass curves space time is simply an intuitive observation and not an explanation for why that happens.

 

[Dale]

Just a slight correction for accuracy, the EFE allows us to calculate the effects of the curvature. Nothing in the EFE explains why there is a curvature.

There is a curvature because there is some stress-energy. The EFE explains that.

I think that you are looking for a non-scientific explanation because the EFE gives a complete scientific explanation for spacetime curvature, the acceleration of objects initially at rest, and all of the other little points that you have brought up.

What type of an answer are you looking for? In other words, what would satisfy your idea of an "explanation"?

 

[yogi]

There is a curvature because there is some stress-energy. The EFE explains that.

I think that you are looking for a non-scientific explanation because the EFE gives a complete scientific explanation for spacetime curvature, the acceleration of objects initially at rest, and all of the other little points that you have brought up.

What type of an answer are you looking for? In other words, what would satisfy your idea of an "explanation"?

It doesn't explain anything at all - curvature is Einsteins way of justifying gravity - there was no physical mechanism that could explain why separated masses attracted one another so Einstein postulated that inert matter conditions space and affects the passage of time. That these conditions (slowed time and curved space) are consistent with the measured value of the gravitational force AFTER YOU HAVE INSERTED THE MEASURED VALUE OF G, does not not necessarily mean they are the cause of gravity - they could be a consequence of a more fundamental condition of which they are descriptive - but not necessarily primary.

 

[Dale]

So what? The possibility of a deeper explanation doesent negate a shallow explanation. Like any two-year-old you can always ask another "why" question. But that doesn't erase the previous answer.

 

[yogi]

So what? .

SEW BUTTONS

The breakthrough of GR is in the recognition that there is no such special thing as "Gravitational Mass"

Here is a statement by the great man himself: "The theory avoids all internal discrepancies which we have charged against the bases of classical mechnics...it allows the treatment of the problem of motion of material points of practically negligible mass in the gravitational field...it does not take into account the reaction of the moved material points on the gravitational field nor does it consider how the central mass produces this gravitational field"

 

[Dale]

The breakthrough of GR is in the recognition that there is no such special thing as "Gravitational Mass"

I think that you are also looking for a non-scientific explanation because the EFE gives a complete scientific explanation for spacetime curvature, etc.

I will ask you the same question I asked slcoleman:

What type of an answer are you looking for? In other words, what would satisfy your idea of an "explanation"?

 

[yogi]

I hate to be put on the spot by someone named after unwanted email - but here goes

Everyone knows there will always be one more question - ultimate reality will most likely never be known - but in the case of gravity - I would settle for a tie to other physics. - Einstein himself realized this to be aweakness of the theory - ...while he was confident about Riemannian curvature, and referred to the left half of the equation as made of fine marble, he was never happy with the right side - he called it a house of straw - there was no physics to indicate why throwing all sorts of energy into the right half would affect distant space - granted the equation works - but lying somewhere to be discovered is the connection between matter and geometry and somewhere a reason why G has the value it does.

Cheers

 

[Dale]

but in the case of gravity - I would settle for a tie to other physics.

It is certainly true that GR is not a TOE, but as a theory of gravity it is completely adequate scientifically. The desire to tie it into other theories is a philosophical preference. It is, IMO, a good philosophical stance, as important to the philosophy of physics as Occham's razor, and one that has been fruitful for other theories. But I recognize that as a philosophical preference (one that you and I share) and not a scientific requirement.

granted the equation works

That is the only scientific criteria that any theory has to meet.

 

[CRichard]

OK, sorry to bring this topic back up, but I just was rereading Relativity Visualized and had a question. If the right idea is that mass distorts spacetime in such a way as to cause gravity, is it true that the distortion of time is the only thing that can cause an apple to fall from your hand, if it begins at 0 speed (since its initial 0 velocity stops space from affecting it)? Also, since a light beam doesn’t age or pass through time, would the curvature of space be the only factor in its deflection by mass? My main question, I guess, is if an object starting with no speed in space experiences the same gravitational acceleration (9.81 m/s^2) as a light beam passing Earth with no speed through time, but only because the former is affected only by warped time, and the latter is only affected by warped space, and that these effects are equal. Also, would something in the middle, like an object that you somehow threw at half the speed of light by Earth, undergo the same gravitational acceleration, because warped time and warped space each exert half their influence but affect the object simultaneously so as to produce the correct acceleration?

 

[cosmik debris]

Yogi, G is a coupling constant and it is used to change units of measure. It allows mass to be expressed a length, just in the same way as c allows time to be expressed as a length. You can set them to 1 and work in Planck units if you like. Yes, if you want a value in SI units you will have to measure it just as you do with c. There are also dimensionless constants (26 according to John Baez). These constants are used in the most accurate of all theories, QFT. Sure no-one knows why they have the values they do, or how to compute them from the theory, and that may mean the theory is incomplete in some sense, but it is the same with all theories.

 

[Phrak]

Epstein's reasoning is then that you can fold this paper into a cone (which is allowed because it doesn't change the nature of spacetime) and then see that the straight line actually curves toward the wider end of the cone. This is how gravity comes about.

If I understand you correctly, this seems to violate time symmetry.

 

[TurtleMeister]

I enjoyed the debate between yogi and DaleSpam concerning the value of G.

Your missing the whole point - whatever units we use to express G - it will always measure the same - G appears to be temporally constant irrespective of the dimensions we use - but the units are significant - they show the fundamental tie between the physical thing (i.e., the law of Gravity) and its relationship to the cause that brings about the multiplying factor needed to make experimental measurements conform to the underlying theory. In the case of G, the units are cubic meters per sec squared per kgm - i.e., volumetric acceleration/kgm. And the volumetric acceleration of the universe within the limits of experimental error comports with the experimentally determined value of G - that is not numerology - it comes directly from Freidmann's equation.

That was the best explanation for G that I have read. Not to say that I think DaleSpame is wrong. What he is saying is of course correct, but it's not what makes the value of G meaningful.

Here is a case in point. The equivalence principle tells us that $m_i = m_p = m_a$. If we could somehow change the ratio of $m_a$ to $m_p$ / $m_i$ then the measured value of G would change also, no matter what choice of units we used. In fact, this is precisely the way the equivalence principle can be experimentally tested. An example can be found in: "Experimental Measurement of the Equivalence of Active and Passive Gravitational Mass - L. B. Kreuzer". Start reading at the section titled "II. Theory".

Thanks for the interesting thread.