Anilkumar

Not really a question of physics.

 

That would be a preconceived notion applied to the situation. Experimentally we see that it is indeed true.

Well fine then,

what is the role of Differential Geometry, here?

You will need to "pull apart" the Einstein field equations to understand this in proper detail . . .

Differential geometry . . .

But:

• Experimentally we see that mass bends space.
• Physics is not interested in knowing about the origin [= why/how Mass bends EMPTY Space'.] of 'Geometry of Space or the origin of the 'Influence', for Motion', which also CLEARLY means, that: - 'Differential Geometry has no role in 'telling us' why/how Mass bends EMPTY Space'.
   
  Then what role does 'Differential Geometry' play, here?

I would like to thank,

Scienceforums.net,

for providing this wonderful platform,

where,

a layman could discuss his doubts, with;

highly Informed Persons, who have;

gone to great lengths, to;

acquire that information.

This platform is doing,

a great service to mankind.

May god bless you all, those,

involved in the discussions and;

maintaining this platform.

And also;

the Software involved too is,

just marvelous.

Keep it up,

everybody.

Because a mass will not move or accelerate on its own. There is an external influence, and in GR, this is geometric in origin.

Seems appealing,

But where does the Geometry originate from?

Certainly,

the Space is incapable of providing it.

---------------------------------***********

IamJoseph,

Space & Vacuum are two different things.

But it does. Space is a less rare density of matter. The difference is in degree not in kind:

Does Physics say this?

The geometry of space is inferred or extrapolated from the observed behaviour of bodies within it.

Why don't we accredit, the observed behavior of bodies, to their 'INHERENT PROPERTIES' ?

Why ascribe it to 'NOTHING'?

-------------------------**********************-----------------------------------

. . . Space is a rarer form of matter, rarer than atmospheric matter, as in: solids; liquids; atmospheric matter [less rare; air]; non-atmospheric matter [still rarer - but never 'nothing'] . . .

This does not accord with the definition of Space.

Thanks Quenter,

for your concern.

There is a way, Anilkumar. The Friedmann-Robertson-Walker cosmological model is derived from the einsteinian equations. Here the mass density is thought homogeneous like sugar in the tea. Being perfectly structureless, the curvature as expressed by the sum of the angles in a triangle can be hyperbolic, euclidian or spherical. Depending on the mass density.

 

@IM Egdall: "As to why mass/energy causes the warping of spacetime -- I think we need new physics to answer that."

 

Why? There is no need, as long as the predictions of the theory are in excellent agreement with the observation. The problem of General Relativity is the singularity.

To act, one needs 'SOMETHING' to act on;

one cannot act on 'NOTHING' ;

SPACE is 'NOTHING' ;

it is 'EMPTINESS'.

Mass or mass density, denotes EXISTANCE of physical material, and Empty-Space denotes NON-EXISTANCE of anything.

Then,

how can something that 'exists' act on something that 'does not exist'.

The very proposition that Space i.e. 'INFINITE - EMPTINESS' has a geometrical shape of its own, is incomprehensible.

How can empty space, have a geometrical shape? It is like saying 'The Non-existent', 'THE-ABSENT', or 'THAT WHICH IS MISSING' has a shape of its own.

If you do a series expansion of the relativistic KE equation, the first term is mv^2/2. The relationship at low energies was unchanged, to a fairly high degree of precision.

The new version came in because,

the older version had shortcomings.

I just meant to say that, our perceptions change as new observations come in.

I would like to keep away from any contention.

I'm not sure how this would happen. Past results cannot be causally changed by future observations. That limits what changes you can get in a law. You can find that in some set of cases it doesn't apply or needs to be modified.

 

From a more semantic point, if we discover that some law varied, then it wasn't actually a law.

Before 1905,

the Kinetic Energy was given by the Formula;

E=mv²/2.

After 1905,

it had to be altered to;

E=mc²g-mc².

You are close. However, it is not quite correct to say "gravity warps space." It is better to say the presence of mass/energy warps space (and time). LIke the presence of the Sun warps space and time in its vicinity.

 

And this warping or curvature of space and time (spacetime curvature) is what causes planets to orbit the Sun and holds us down to the Earth. We call this effect gravity. So spacetime warp or curvature IS gravity.

 

Physicist John Archibald Wheeler said something like "mass/energy grips spacetime and tells it how to curve -- and curved spacetime (gravity) grips mass/energy and tells it how to move."

If it is right to say that;

"Gravity influences Motion & Time"

Why are we creating unnecessary misunderstanding by saying, the other way round, that;

"Presence of mass/energy warps space &Time. And this warped space affects motion. This effect is called gravity".

While we very well know that;

• Space is a structureless entity. And so altering the structure of that entity which does not have any structure does not arise.
• We do not know how it can be done.

As to why mass/energy causes the warping of spacetime -- I think we need new physics to answer that. Maybe the combining of general relativity and quantum mechanics in a new theory of so-called "quantum gravity" will someday tell us why.

Replacing the rocket by radar signals, we talk about the Shapiro Delay. Those signals reflected by mars take more time to return to earth in case they pass near by the sun than compared to an analogous measurement without the sun. The effect is tiny but measurable and demonstrates the spacetime curvature due to the sun.

I have no objection in the fact that the path & duration of the signals are altered.

But I have objection in how we say that.

We say that;

"mass/energy warps Space & Time and so, the Signals take the altered path".

I object this method of its interpretation, because, Space is a structureless entity. And there is no way, the structure of a structureless entity can be altered.

So instead I want us to say that;

"Mass has Gravity. And this Gravity alters the Direction and Duration of anything that is moving, in its vicinity"

An accelerating electric charge gives rise to electromagnetic wave just as an accelerating massive body gives rise to gravitational waves. the static object will not give off waves

 

 

 

They follow from General Relativity - and I believe it was Einstein who first predicted their existence

 

 

 

Orbital energy is the sum of the total (ie both bodies) kinetic energy and the total potential energy of a two body system in orbit around each other (or around a central point).

[math] \epsilon_{orbital}= \epsilon_{kinetic} + \epsilon_{potential} = \frac{(orbital velocity)^2}{2} - \frac{G(sum of masses)}{radius} [/math]

 

This sum stays constant - unless energy is either added or removed from the system. One method of removing energy is the emission of gravitational waves. Waves carry energy (and other properties) out of the system. A reduction in the sum of energies causes the orbiting bodies to spiral into each other and get faster. In the case of the neutron stars mentioned we have been able to detect the speeding up of the orbital rotation.

 

 

 

To slightly clarify and expand on Janus's excellent answer - some accelerations, periodic motions, and behaviours give rise to gravitational waves and others do not. the earth - sun system will radiate gravitational waves due to earths orbit, but the earth's mass spread out into a disc around the sun whilst still orbitting (think asteroid belt) will not radiate. The earth will not radiate due to its rotation on its own axis (save the infinitesimal amount that the earth is not symmetrical about axis of rotation) but a tumbling irregular planetoid will radiate. When there is spherical/cylindrical symmetry then the acceleration/behaviour is unlikely to cause gravitational waves

Thank you Imatfaal,

for the exhaustive explanation.

Continuous conservation laws stem from symmetries. Energy being conserved is tied to time-translation symmetry, i.e. the laws of physics are constant in time.

I feel the Universe & its contents behave not according to Laws of Physics. But they behave according to their inherent properties.

The Laws of Physics are formulated according to the observations of the behavior.

When our ability to observe/interpret, enhances/changes; the the Laws of Physics are prone to change.

But the properties of the Universe & its contents remain the same.

The second statement is not only atrocious, it is quite wrong. Energy is released in forming bonds.

I regret. That was a mistake. I should have typed 'formed' instead of 'broken'.

Hi anilkumar I see you've posted on my thread that "theory" explains it. As for the maths I'd need alot of help 2 express.

I feel 'Theory' gives a feel of whats happening.

And Mathematics gives a proof of it.

Thank you very much Janus,

for the painstaking explanation.

. . . Any mass that accelerates or follows a periodic motion produces gravity wave . . .

Does this mean that;

"If there is an isolated mass, which is static; it would exhibit Gravity but would not radiate Gravitational waves"?

Back to the orbiting neutron pairs, they are losing energy at a rate consistent with that predicted by the emission of Gravity waves.

• The Gravitational waves have not been detected yet.
• There is no concrete evidence to show that they are a form of energy.

Does this mean that the existence of Gravitational waves is a Hypothesis?

What prompted this Hypothsis?

. . . In the case of the orbiting neutron stars this energy comes form their orbital energy. This is why they are approaching each other . . .

What does Orbital energy mean?

Could you please elaborate on how Orbital energy is related to the approaching of the pair of Neutron stars?

. . . Be careful not to confuse gravity waves with the gravitational force or field. They bear the same relationship to each other as do the light emitted by a flashlight and the magnetic field of a magnet.

 

Electromagnetic waves (light, radiowaves, etc) carry information about changes in electromagnetic fields, and gravity waves carry information about changes in gravity fields . . .

Thank you for the kind forewarning. This was very informative.

As to the rocket, once the earth is put in place near the two points, both space and time are affected (warped.) The rocket would then follow the shortest path in the warped spacetime or what is called the geodesic.

 

As to why mass/energy causes the warping of spacetime -- I think we need new physics to answer that. Maybe the combining of general relativity and quantum mechanics in a new theory of so-called "quantum gravity" will someday tell us why.

OR

simply,

are we interpreting the effect of the Gravitational field on Matter & Time as Space-time warp? i.e.;

When an object or light is passing through a Gravitational field it is forced to behave differently due to its influence and we are attributing this change in behaviour to a change in the structure of the Space.

To make my point clear, I would like to give the following illustration:-

"Let us suppose there is a Bar-magnet and a Magnetic-needle, in empty space, devoid of any influence of any other kind. The Magnetic-needle is placed far away from the Magnet & there is negligible or no deflection of the needle.

Now the Magnetic-needle slowly starts moving towards the Magnet. As it gets closer to the Magnet, we start seeing deflections in the needle.

Now we know that the deflections are due to the influence of the magnetic field of the Bar-magnet.

But instead of saying that the deflections are due to the influence of the magnetic field of the Bar-magnet; we say the Space arround the Bar-magnet is warped due to its Magnetic-field & the warp is the cause for the deflections".

Is this similar to Space warp due to Gravity. The difference being that, the Magnet deflects the Magnetic-needle, whereas Gravity deflects everything with mass & even Time.

Like saying;

if there is a Ball on top of a Table. Instead of saying 'The Ball is on the Table' we say 'The Table is under the Ball'.

Instead of saying 'Gravity influences Motion' we say 'Gravity warps Space'.

With all this writing as above;

Am I anywhere near interpreting the phenomenon of Space-Time warp?

I have taken the liberty of emphasizing different words from part of what you quoted

 

Wikipedia says -

 

'In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure'.

 

'In classical mechanics, energy is a conceptually and mathematically useful property, as it is a conserved quantity'.

 

Bingo. Useful, as noted above, because it is conserved within a reference frame.

 

The m in E=mc^2 refers to mass

Though many in number, these different credentials, fail to give an indepth meaning of the Omnipotent & Omnipresent entity.

What are the intricacies involved in & the rationale in support of, the affirmation that, "It is useful because it is a conserved quantity "?

If it is the property of Matter or Mass, what makes it, to be recognized as a property of Matter/Mass.

There are contradictions also, like;

"Matter is annihilated & converted into energy"- which shows that both are two different manifestations of the same thing.

AND

"Energy is held inside Matter as Bonds between particles and molecules. If these Bonds are broken, energy is released" - which gives the impression that they are two different things.

E=MC2 says energy and matter are the same . . .

It also shows Energy is a produce of mass.

So then, please supply me one cubic meter of Joules.

Thank you DrRocket,

for connecting.

Can we produce Energy without Matter?

The inability of man to do somethings, sure, does prove certain things. But is not an adequate explanation in itself.

Neither spacetime nor energy are substances.

Energy - Not a substance?

Wikipedia says -

'In physics, energy is an indirectly observed quantity'

'In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular or aggregate structure'.

'In classical mechanics, energy is a conceptually and mathematically useful property, as it is a conserved quantity'.

'In Relativity, the amount of energy is directly proportional to the mass of body'

And lastly;

'Energy density is a term used for the amount of useful energy stored in a given system or region of space per unit volume'

And there is also a definition for Substance/Matter as follows;

'Matter is a general term for the substance of which all physical objects consist. A common way of defining matter is as anything that has mass and occupies volume'.

So from all the above we can infer that Energy has mass & and volume. So it has to be a Substance, I suppose.

If not, what is it?

I have read somewhere that it is a property.

Please explain.

Edit: Italics.

There is indirect evidence in the form of a pair of orbiting neutrons stars. Theory says that they should radiate energy away in the form of gravity waves, and this should cause them to spiral closer to each other. Careful measurements have shown that they are approaching each other at the same rate as predicted by gravity wave emission. Not yet. but this is not surprising as they would be very weak and it takes extremely sensitive equipment to detect. They travel at c and are essentially "ripples in space".

Why the sources of Gravitational waves are only the "pair of orbiting Neutron stars"?

Is there any evidence to show that Gravitational waves are actually a FORM of ENERGY?

If so;

and "Because energy can not be created. It can only be converted from one form to another" ;

what "FORM" of "ENERGY" is being converted into Gravitational energy in a pair of orbiting Neutron stars? i.e. what is the BASIC - SOURCE of Gravitational energy? or "WHAT" can be CONVERTED into Gravitational energy.

Yes.

Isn't that amazing?

Think about it twice.

Yes. It is the most mysterious thing in the universe.

And, is there any empirical evidence for the existance of Gravitational waves?

Have they been detected?

If so, how do they behave?

The relativists say they exist.

I don't see there is a contradiction. Einstein was not an expert in differential geometry when he first worked on developing general relativity. Grossmann introduced Einstein to differential geometry and collaborated with Einstein on several papers. It was Levi-Civita who suggested to Einstein that differential geometry, and in particular tensors and the idea of general covariance could be useful in his formulation of a relativistic theory of gravity.

 

The earliest works of Einstein on gravity, well really acceleration and free fall in special relativity (1908) and then later the equivalence principle and the prediction of gravitational time dilation (1911) all pre-date the proper formulation of general relativity.

 

 

The point being, Einstein realised that general relativity requires differential geometry to be formulated properly. The motivation for this is that Einstein believed physics to be described by local fields and that covariance is fundamental. Grossmann played a big role in helping Einstein with geometry.

Yes, even I too had read something similar to what you mentioned.

Thank you DrRocket,

for your interest.

Mathematics is the language of physics.

I feel, a language can not invent theories. It is the mind that invents theories. And languages are usefull in expressing it to others.

Also, I am unable to decide which one of the following two statements are true, as they are contradictory:-

. . . . .It was ony because Riemann had invented differential geometry that Einstein was vable to formulate genersal relativity . . . .

. . . . It was specifically the application of differential geometry and tensor analysis that enabled Einstein to formulate general relativity.

------------------------------------And

I don't think Einstein was an expert in differential geometry when he formulated general relativity. My understanding is that he realised that differential geometry was likely to be important, so he made the effort to learn what he could.

 

Differential geometry at the time was the realm of pure mathematicians, only later has it become a standard part of the physicists tool kit . . . .

Anyway I am not an authority on this and moreover I am very-less interested in knowing HOW & much-more interested in knowing WHAT, Einstein invented.

I started this thread to get a glimpse of the Space-time warp phenomenon. To know the HOWs & WHATs of it. I want to get to know about it as much as possible. I do not wish to become an expert or an advocate of SR/GR. I want to know about it.

I would appreciate if anybody could help me in this regard.

Thank you.

I don't think Einstein was an expert in differential geometry when he formulated general relativity. My understanding is that he realised that differential geometry was likely to be important, so he made the effort to learn what he could.

 

Differential geometry at the time was the realm of pure mathematicians, only later has it become a standard part of the physicists tool kit.

 

 

 

Well, mathematics is the framework of all physical theories.

 

 

 

Simply is a very subjective and this is an idealisation. To really explain general relativity "simply" one does require some knowledge of differential geometry. Maybe one does not need all the details to get the idea, but some elementary understanding of manifolds, metrics and connections is needed.

 

We all have recommendations on what books to read, I suggest Sean M. Carroll, Lecture Notes on General Relativity, arXiv:gr-qc/9712019v1.

Hello ajb,

I am trying to learn differential geometry. But till then I think I can surely, get to know about it theoretically as much as possible.

Nice meeting you.

At the risk of oversimplifying, I will try to answer your question with no mathematics. The presence of mass (and energy) causes space and time to warp. This is at the heart of general relativity. Let's look at examples of each:

 

 

Space warp: Imagine two points in space where all objects are so far away that gravity is virtually zero. Now imagine placing the Earth near these two points. As seen from far away, the two points will now be a different distance apart. This in essence is space warp or space curvature.

 

Time warp: Imagine a clock also in space where all objects are so far away that gravity is virtually zero. Now again imagine placing the Earth near this clock. The clock now runs slower. due to the Earth's presence. This is called time warp or curvature of time.

 

Together time warp and space warp are called spacetime curvature. And this spacetime curvature determines the path of the Moon around the Earth, and all the planets around the Sun etc., and holds us to the surface of the Earth. Spacetime curvature IS gravity.

 

I hope this helps.

Hello IM Egdall,

thank you for trying to help-out,

So now,

In the example of Space warp:

If there was a Rocket, shuttling between those two points at a fixed uniform velocity, prior to our bringing Earth near them;

will now take less time or may be more time, to reach between the points, after we place Earth near them?

for the person observing from far away.

If this is so; {I know that there are no WHYs in physics, but still}

is there a reason for this?

i.e.

What TOOLS does Gravity have in its pockets, to change that distance? &

What are the,

OR

Where are the,

nuts & bolts placed in the 'BODY' of "THE 'EMPTY' SPACE", that the Gravity 'tightens' or 'loosens' to bring a STRUCTURAL change in the STRUCTURELESS STRUCTURE of the empty Space?

Thank you

Hi Anilkumar:

Let me try to explain in layman terms as why space around a mass is curved.

It is gravitational field that establishes this so called curvature around a mass. And the reason is because gravitational field is composed of two forces. Which coexist and cooperate at 180 degrees relative to one another. And these two forces divided the space equally between themselves, while at the same time they have to remain perpendicular to one another at all the times. And as a result, at both polar ends they become subtracted, and this subtraction results in the curvature of space at both poles. Which makes the curvature of the field something similar to magnetic field lines.

Hello Divinum1,

great many thanks for connecting;

• 'gravitational field is composed of two forces' - I did not know this clearly. Is this what they say, that - One component is directed towards the center & the other is in a direction tangential to the cirular orbit?---------------------------------------------------------------------------------------------------
• 'polar ends' - Does this mean; the polar ends of the earth or any body [the north/south pole]?------------------------------------------------------------------------------------------------------------------------------------------------------------
• 'they become subtracted' - Vector subtraction?----------------------------------------------------------------------------------------------------------------------------
• 'Which makes the curvature of the field something similar to magnetic field lines' - So due to the curvature of the the Gravitational field, things moving through that field, tend to follow the curved lines of Gravitational field, like a magnetic compass needle gets deflected along the magnetic lines in a magnetic field?

Thanks.

Now that you think you have understood how things are going, just figure:

I am not pushing you any more: I am attracting you (1) from a distance (2).

(1) how is that possible? I am not a magnet and you are not made of steel.

(2) how is that possible? How can a force act "magically" through distance ?

That's the beauty of gravity.

There is a force of attraction between any two objects with mass according to Newton's 'Law of universal Gravitation';

Given by :-

----------------F=GMm/r²

Edits: Grammar

This is the most wonderful thread I have seen since my arrival here. I am touched. (no sarcasm)

For the first time, I have spend my available amount of + reputation for the day, I didn't even know there existed a limit.

Sorry Michel123456,

I forgot to thank you personally,

You gave me the first break by,

pushing me sideways,

while I was walking on the street in a straight line;

Wait a moment. If you walk on the street on a straight line, and I come to push you from the side, will you change direction or not?

Yes. It's why a space capsule/shuttle an dock with the ISS, even though that have different masses. They can be put into essentially identical orbits.

You (Anilkumar) might want to hear from me, and so, I agree with what has been discussed about these cannonballs/docking scenarios.

Fantastic;

& that last piece of information, nice one, 'the docking process';

Swansont, Ewmon;

you're great;

Thank you both & everybody, for being with me.