Warped spacetime and gravity

[Santalum]

Something just occured to be with this.

 

In the analogy of the elastic membrane and heavy objects warping the surface such that smaller objects circle the heavier one around the indentation it creates in the membranes requires a force (gravity) to elicit that circular movement around the indentation.

 

If mass causes an analogous indentation in the fabric of spacetime then wouldn't there need to be a force to cause another object to move around the 'indentation'.

 

Is the warped spacetime thing meant to explain the behaviour objects under the influence of gravity or the nature of gravity itself?

[D H]

If mass causes an analogous indentation in the fabric of spacetime then wouldn't there need to be a force to cause another object to move around the 'indentation'.

The rubber sheet analogy is just that -- an analogy aimed at the law audience. Don't try to read anything more into any one of those analogies than the limited thing the analogy is trying to depict. All of these analogies (the rubber sheet model, the expanding balloon model, the raisin bread model) are ultimately flawed in one way or another. In this case, what this rubber sheet analogy is trying to depict is that spacetime is not the simple model used Newtonian mechanics. Take it to say anything more than that and you are reading too much into it.

 

If you want to go past the analogies you need to learn the mathematics and physics.

[ydoaPs]

Obligatory xkcd:

 

 

The rubber sheet analogy is just that -- an analogy aimed at the law audience. Don't try to read anything more into any one of those analogies than the limited thing the analogy is trying to depict. All of these analogies (the rubber sheet model, the expanding balloon model, the raisin bread model) are ultimately flawed in one way or another. In this case, what this rubber sheet analogy is trying to depict is that spacetime is not the simple model used Newtonian mechanics. Take it to say anything more than that and you are reading too much into it.

 

If you want to go past the analogies you need to learn the mathematics and physics.

 

Indeed. It's fun math too. Yay tensor fields!

Edited February 27, 2012 by ydoaPs

[Santalum]

Obligatory xkcd:

 

 

 

 

Indeed. It's fun math too. Yay tensor fields!

 

 

But to begin with can you answer this question?

 

Is the warped spacetime thing meant to describe the behaviour objects under the influence of gravity or the nature of gravity itself?

[ajb]

A recent blog post of mine may be of interest. You can find it here.

[ydoaPs]

But to begin with can you answer this question?

 

Is the warped spacetime thing meant to describe the behaviour objects under the influence of gravity or the nature of gravity itself?

 

The idea is that gravity is a change in geometry from euclidean space. Things traveling in a straight line from the reference frame of the traveler appear to be traveling in an arc from an outside reference frame.

[StringJunky]

a·nal·o·gy ( -n l -j ). n. pl. a·nal·o·gies. 1. a. Similarity in some respects between things that are otherwise dissimilar.

 

I liked your article AJB...well-written and presented. Nice one.

[Santalum]

The idea is that gravity is a change in geometry from euclidean space. Things traveling in a straight line from the reference frame of the traveler appear to be traveling in an arc from an outside reference frame.

 

With respect that is not precisely anwering my question.

 

Is the change in geometry of spacetime source of gravitational force or is it merely a convenient way of describing the movement of the objects under the influence of gravity source is not at issue?

 

I guess my question goes to that long debate that was previously had with that fellow who figured he was going to single handedly re-write the theory of relativity.......not that I don't accept that spacetime can be warped..........

 

But on second thoughts something as seemingly abstract as charge, with like charges exerting a repulsive force.........., then there is no reason not to beleieve that warped spacetime cannot similarly be the source of gravity even though it makes no logical sense in terms of the elastic membrane analogy.

Edited February 27, 2012 by Santalum

[ydoaPs]

With respect that is not precisely anwering my question.

 

Is the change in geometry of spacetime source of gravitational force or is it merely a convenient way of describing the movement of the objects under the influence of gravity source is not at issue?

 

I guess my question goes to that long debate that was previously had with that fellow who figured he was going to single handedly re-write the theory of relativity.......not that I don't accept that spacetime can be warped..........

 

The change in spacetime geometry IS gravity. If you look at the equations, the left hand side is represents the geometry and the righthand sign is the mass-energy. Gravity doesn't cause spacetime geometry to deviate from Euclidean space. Gravity is the deviation from Euclidean space due to energy.

[Santalum]

The change in spacetime geometry IS gravity. If you look at the equations, the left hand side is represents the geometry and the righthand sign is the mass-energy. Gravity doesn't cause spacetime geometry to deviate from Euclidean space. Gravity is the deviation from Euclidean space due to energy.

 

 

But on second thoughts something as seemingly abstract as charge, with like charges exerting a repulsive force.........., then there is no reason not to beleieve that warped spacetime cannot similarly be the source of gravity even though it makes no logical sense in terms of the elastic membrane analogy.

 

One takes charge for granted when one learns about it at school........

 

But what is charge exactly and WHY does it exert or create a force.

 

Same reasoning......what is gravity and why does warped spacetime create it.

Edited February 27, 2012 by Santalum

[ydoaPs]

Same reasoning......what is gravity and why does warped spacetime create it.

 

Gravity doesn't cause spacetime geometry to deviate from Euclidean space; it is the deviation from Euclidean space caused by energy. And that's largely the point of the analogy in question.

Edited February 27, 2012 by ydoaPs

[D H]

Same reasoning......what is gravity and why does warped spacetime create it.

Space-time does not create gravity. A much better to look at it is "Mass tells space-time how to curve, and space-time tells mass how to move." (John Wheeler)

 

As to why "mass tells space-time how to curve," general relativity doesn't say. General relativity describes what happens. Why this happens is a mystery left to future generations. Some physicists and mathematicians are working on this problem (I believe ajb is one such person), but the problem is a rather vexing one.

[Santalum]

Gravity doesn't cause spacetime geometry to deviate from Euclidean space; it is the deviation from Euclidean space caused by energy. And that's largely the point of the analogy in question.

 

Ahhh OK.

 

I don't pretend to fully comprehend it but bringing 'energy' (more specifically concentrated energy in the form of mass) into this discussion sort of adds a new 'dimension' of understanding for me.

[IM Egdall]

Ahhh OK.

 

I don't pretend to fully comprehend it but bringing 'energy' (more specifically concentrated energy in the form of mass) into this discussion sort of adds a new 'dimension' of understanding for me.

 

Per E=mc^2, mass and energy are equivalent. In other words, both mass and energy produce the same physical effects. So both mass and energy produce gravity. And per general relativity, gravity is spacetime curvature (the global warping of space and time by mass/energy).

 

The mass of the Sun, for example, produces spacetime curvature (gravity) in its vicinity. The energy of the Sun (its photons) also produces spacetime curvature (gravity) in its vicinity.

[ajb]

As to why "mass tells space-time how to curve," general relativity doesn't say. General relativity describes what happens. Why this happens is a mystery left to future generations. Some physicists and mathematicians are working on this problem (I believe ajb is one such person), but the problem is a rather vexing one.

 

Why is probably not a question we can ever really understand. What we can do is model gravity and understand things in that context. So, we do know how matter courses space-time to have a non-trivial local geometry. This is the Einstein Field Equations. General relativity has been tested to some huge degree of accuracy. To date there are no observations or experiments that disagree with general relativity.

 

However, we do not expect general relativity to be the final word. In particular general relativity does not take in to account quantum physics. It is expected that on the smallest scales that the notion of space-time will be very different to our understanding via general relativity. But this is probably another story.

[D H]

Why is probably not a question we can ever really understand.

Well, sure. What can be done is to give a slightly deeper meaning. I was using "why" in the lay sense of "what makes that happen?" Physics has deep answers to these "why" kinds of questions with regard to electromagnetism -- but not yet with gravitation.

 

 

What we can do is model gravity and understand things in that context. So, we do know how matter courses space-time to have a non-trivial local geometry. This is the Einstein Field Equations. General relativity has been tested to some huge degree of accuracy. To date there are no observations or experiments that disagree with general relativity.

That is what I meant when I wrote "General relativity describes what happens."

 

However, we do not expect general relativity to be the final word. In particular general relativity does not take in to account quantum physics. It is expected that on the smallest scales that the notion of space-time will be very different to our understanding via general relativity. But this is probably another story.

That "other story" is (I think) what Santalum was asking about. Physicists don't know that "other story" yet. Right now we're stuck with descriptive models such as general relativity. Deadly accurate, but still just descriptive.

 

@Santalum: That next step that people such as ajb are researching will most likely still be a descriptive model. Quantum mechanics is in a sense a deeper model than general relativity, but it still is ultimately just a descriptive model. Quantum mechanics, for example, can't answer why the fine structure constant or the other fundamental unitless constants have the particular values that they do have.

[MigL]

I would say that the 'change in geometry of spacetime' is not 'the source of gravitational force', rather the geometry of spacetime IS gravity, which then influences the 'motion of objects'. I believe that's the question you asked.

The rubber sheet analogy does work, as long as you remember that its basically a 2d representation. Most shopping malls have funnel like devices ( intended to collect money for charities ) where a child can pitch in a coin, and it will slowly spiral down into the collector. If there was no friction between coin and funnel/air, I'm sure you could set up a stable orbit for that coin. Just like in the universe at large.

 

It seems, AJB, that most effort is put into making GR comply with QM to acheive unification. Meanwhile Loop Quantum Gravity seeks to constrain QM with GR ( like the abolition of an absolute spacetime frame ), yet its not discussed as much as say, Sstring theory, even though it has no need for supersymmetry and additional dimensions. Trying to gain even a basic understanding of the theory is a bear because of the formidable math involved. I don't want to hijack this thred and incur Swansot's wrath, but maybe if you or another member is familiar with the subject, you could start a separate thread/tutorial.

[ajb]

It seems, AJB, that most effort is put into making GR comply with QM to acheive unification. Meanwhile Loop Quantum Gravity seeks to constrain QM with GR ( like the abolition of an absolute spacetime frame ), yet its not discussed as much as say, Sstring theory, even though it has no need for supersymmetry and additional dimensions.

 

That is a valid point. It is true that more people work in string theory than than say loop quantum gravity or other canonical approaches to quantum gravity.

 

Physics has deep answers to these "why" kinds of questions with regard to electromagnetism -- but not yet with gravitation.

 

The biggest difference is that we have a very good quantum theory of electrodynamics.

[Santalum]

Space-time does not create gravity. A much better to look at it is "Mass tells space-time how to curve, and space-time tells mass how to move." (John Wheeler)

 

As to why "mass tells space-time how to curve," general relativity doesn't say. General relativity describes what happens. Why this happens is a mystery left to future generations. Some physicists and mathematicians are working on this problem (I believe ajb is one such person), but the problem is a rather vexing one.

 

I understand what you mean.....'causes' is a bad choice of word as there are unintended conotations associated with it.........as in the indentation in the elastic membrane causes things to move in a curved path due to another force.

 

(its photons) also produces spacetime curvature (gravity) in its vicinity.

 

I would assume to a lesser extent due to the fact that energy is more diffuse compared to matter.

 

Why is probably not a question we can ever really understand. What we can do is model gravity and understand things in that context. So, we do know how matter courses space-time to have a non-trivial local geometry. This is the Einstein Field Equations. General relativity has been tested to some huge degree of accuracy. To date there are no observations or experiments that disagree with general relativity.

 

However, we do not expect general relativity to be the final word. In particular general relativity does not take in to account quantum physics. It is expected that on the smallest scales that the notion of space-time will be very different to our understanding via general relativity. But this is probably another story.

 

 

Yes, I have been watching a number of documentaries about this. Particularly about Einstein's in vain attempts to discredit quantum mechanics right up until his death.

 

@Santalum: That next step that people such as ajb are researching will most likely still be a descriptive model. Quantum mechanics is in a sense a deeper model than general relativity, but it still is ultimately just a descriptive model. Quantum mechanics, for example, can't answer why the fine structure constant or the other fundamental unitless constants have the particular values that they do have.

 

Same sort of question as why does the circumference of any circle divided by its diameter always equal exactly pi.

 

Facinating mysteries of the cosmos.

Edited February 27, 2012 by Santalum

[D H]

Same sort of question as why does the circumference of any circle divided by its diameter always equal exactly pi.

Not at all! What you said is essentially the definition of pi, only holds in Euclidean geometry, and it is not a mystery. That the ratio of circumference to diameter is the same for all circles on a Euclidean plane is a mathematically provable concept. Science and mathematics are in a sense very different things. The proof that ratio of circumference to diameter is the same for all circles on a Euclidean plane is valid forever. Finding some non-Euclidean surface for which the ratio of circumference to diameter is not constant does not dislodge that proof. Scientific theories, unlike mathematical theorems, cannot be proven to be true. Scientific theories can however be demonstrated to be false. All it takes is one experiment that shows that the universe operates otherwise.

[DrRocket]

 

The biggest difference is that we have a very good quantum theory of electrodynamics.

 

We have a theory of quantum electrodynamics that has given some exquisitely accurate explanations for things like the anonalous magnetic moment of the electron.

 

We also have a very good theory of gravitation that has given accurate predictions of the precession of the perihelion of Mercury, and predicted previously unanticipated phenomena such as gravitational lensing and black holes.

 

I would hesitate to call either theory "deeper" or more profound than the other.

 

What is abundantly clear is that the two theories are fundamentally incompatible -- one is stochastic and the other is deterministic.

 

General relativity is apparently mathematically consistent, or at least is well-defined and no inconsistencies are known. But it does admit singular spacetimes that may well not be representative of reality.

 

Quantum electrodynamics is not so blessed, and I think it would help a bit if it could be put on a more satisfying mathematical basis. Nevertheless it seems to contain in its essence of much of the physics of everyday life -- the physics governed by the electromagnetic force -- which in principle includes chemistry and biology. On the other hand the quantum vacuum is not well understood. Those predictions that are finite, made in an attempt to explain the cosmological constant that is consistent with astronomical observations, are off by a factor of something like 10^120. Moreover, the equations ar so difficult that as a practical matter it is not useful in explaining anything nearly so complex as chemistry.

 

So I think it is more fair to say that, while a great deal is known of modern physics, even more is not known and an ultimate answer to many questions will have to wait for better theories -- better than either general relativity or the various quantum field theories.

[Santalum]

Not at all! What you said is essentially the definition of pi, only holds in Euclidean geometry, and it is not a mystery. That the ratio of circumference to diameter is the same for all circles on a Euclidean plane is a mathematically provable concept. Science and mathematics are in a sense very different things. The proof that ratio of circumference to diameter is the same for all circles on a Euclidean plane is valid forever. Finding some non-Euclidean surface for which the ratio of circumference to diameter is not constant does not dislodge that proof. Scientific theories, unlike mathematical theorems, cannot be proven to be true. Scientific theories can however be demonstrated to be false. All it takes is one experiment that shows that the universe operates otherwise.

 

Yeah, yeah, yeah.

 

But why Pi on a Euclidean plane?

 

Why an irrational number whose decimal place go on infinitely but never ever repeat......supposedly?

 

I believe that was the point made in "The Code"

[DrRocket]

Yeah, yeah, yeah.

 

But why Pi on a Euclidean plane?

 

Why an irrational number whose decimal place go on infinitely but never ever repeat......supposedly?

 

I believe that was the point made in "The Code"

 

The series

 

[math]\displaystyle \sum_{n=0}^\infty \frac {z^n}{n!}[/math] where [math]z \in \mathbb C[/math]

 

converges abslolutely and uniformly on compacta. It can be shown to define a periodic function, which we call the exponential function. [math] \pi[/math] is defined to be the period of this function divided by 2i.

 

It can be proved that [math]\pi[/math] is not only irrational but in fact transcendental. Therefore its decimal representation does IN FACT neither terminate nor repeat. There is no snide "supposedly" about it.

 

One can also show that in Euclidean geometry the ratio of the diameter of a circle to its circumference is precisely [math]\pi[/math]. This is a matter of logic and rigorous proof. There is no "supposedly" involved here either.

 

You would do better to learn your mathematics from Walter Rudin in, for instance, Real and Complex Analysis than from Dan Brown and the Da Vinci Code.

[I-try]

Santalum, my answer to your question concerning gravity and the indentation in a rubber sheet is as follows. Yes it is only an analogy that directs human thought away from having to imagine orbits to that of a visual experience.

 

The indentation depicts a downhill situation and so to our experiences of gravitational effects. The other effect you refer to is matters inertial property that must be acting under the circumstances dynamically illustrated. For all its pretence of simplicity, practically the whole of physical reality that involves force is included in that illustration.

 

To begin, there is the question as to what constitutes the mass of the orbiting spherical object?

 

What is acting in an attempt to force the moving spherical object towards the central depression?

 

What is compelling the spherical mass to orbit instead of directly rolling downhill?

 

What is enforcing the conservation of momentum and the conservation of energy?

 

 

 

With regards the central effect, science sends conflicting messages. On one hand there is the concept generally believed that the warping of space (what enforces the warping and constitutes the reality of space) causes the effect we call gravity to be only an illusion. On the other hand, there are the constant erroneous references to the pull of gravity or gravitational pull being stated by the Ph D from academia when appearing on TV.

 

 

 

Concerning the inertial ability, the measurement (mathematics) regarding inertia is well documented; even so, the fundamental dynamics as to what circumstances ensures the realities of the laws of motion are not now known by academia.

 

 

 

Some of the statement in the replies to your question state that the fundamental dynamic nature of gravity is not known and may never be known. In that regard, the fact that the General theory of Relativity is considered to be beyond reproach and therefore generally accepted as correct, provides the reason why other concepts of gravity, however logical, unless provided by a well known Ph D, will always be ignored as pseudoscience. My 16 year attempt to have my 160 page work evaluated by those in academia has been met with only two replies thanking me for the offer but stating that they cannot spare the time.

 

If I am asked why I do not explain my concept of gravity on this thread; that is because it would require at least ten pages to do so and I am cautioned not to provide the address to obtain a free download of the published paper.

 

 

[hypervalent_iodine]

I-try: just so you're aware, our friend Santalum was banned sometime ago as a sockpuppet account for another member. He won't be back to respond to you