Curved space

[IamJoseph]

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

 

Why ascribe it to 'NOTHING'?

 

 

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

 

 

This does not accord with the definition of Space.

 

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

 

 

 

Vacuum

From Wikipedia, the free encyclopediaJump to: navigation, search This article is about empty physical space or the absence of matter. For other uses, see Vacuum (disambiguation). Pump to demonstrate vacuumIn everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure.^[1] The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in practice. Physicists often discuss ideal test results that would occur in a perfect vacuum, which they simply call "vacuum" or "free space", and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. The Latin term in vacuo is also used to describe an object as being in what would otherwise be a vacuum.

 

The quality of a vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%.^[2] Much higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth (10⁻¹²) of atmospheric pressure (100 nPa), and can reach around 100 particles/cm³.^[3] Outer space is an even higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average.^[4] However, even if every single atom and particle could be removed from a volume, it would still not be "empty" due to vacuum fluctuations, dark energy, and other phenomena in quantum physics. In modern Particle Physics, the vacuum is considered as the ground state of matter.

 

[Anilkumar]

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?

Edited December 7, 2011 by Anilkumar

[swansont]

Seems appealing,

 

But where does the Geometry originate from?

 

Not really a question of physics.

 

Certainly,

 

the Space is incapable of providing it.

 

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

[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?

Edited December 7, 2011 by Anilkumar

[swansont]

GR tells us how mass curves space, i.e. it gives us the details of the curvature. That's why differential geometry is involved. It does not tell us why this curvature happens.

[Anilkumar]

Great,

 

you have put this in right words,

 

"It does not tell us why this curvature happens".

 

GR tells us how mass curves space, i.e. it gives us the details of the curvature. That's why differential geometry is involved. It does not tell us why this curvature happens.

 

Could you please elaborate on;

 

'What type of details are these?'

 

'Where, i.e., at what juncture, the services of Differential geometry is brought in & for what purpose?'

[swansont]

Great,

 

you have put this in right words,

 

"It does not tell us why this curvature happens".

 

 

Could you please elaborate on;

 

'What type of details are these?'

 

'Where, i.e., at what juncture, the services of Differential geometry is brought in & for what purpose?'

 

It gives you the equations.

[Anilkumar]

It gives you the equations.

 

 

The Einstein's field equations?

[swansont]

The Einstein's field equations?

 

I was thinking of the solutions to them. But at this point you should be talking to someone who is better versed in GR than I.

[IM Egdall]

Anilkumar - May I suggest the following website as an intro to the use of differential geometry in general relativity. Check it out:

 

http://math.ucr.edu/home/baez/gr/

[Anilkumar]

I was thinking of the solutions to them. But at this point you should be talking to someone who is better versed in GR than I.

Thank you Swansont,

 

I am very grateful to you.

 

You let me have a good peep into the 'space-time curvature' premise.

 

But I have a couple of questions more on your last post;

 

Not really a question of physics.

 

 

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

 

Isn't it rational to presume that, Space; being Emptiness, Vacancy, Nothingness – Can not be bent?

 

Anilkumar - May I suggest the following website as an intro to the use of differential geometry in general relativity. Check it out:

 

http://math.ucr.edu/home/baez/gr/

 

Thank you IM Egdall,

 

for your kind gesture.

The link feels amiable.

Edited December 10, 2011 by Anilkumar

[michel123456]

(...)

Isn't it rational to presume that, Space; being Emptiness, Vacancy, Nothingness – Can not be bent?

(...)

 

I always stick to this very simple methodology:

take something in your left hand, take nothing in your right hand. Raise your hands.

Now say you are investigating a crime, and you know the crime weapon is in your hands.

What would be your conclusion?

[swansont]

Isn't it rational to presume that, Space; being Emptiness, Vacancy, Nothingness – Can not be bent?

I had assumed you were speaking of space as a shorthand for spacetime

 

Space ≠ spacetime

 

Spacetime is what is "bent". That is, the geometry of space and time that applies to phenomena is not the same near massive objects as it is far away from them.

[Anilkumar]

I always stick to this very simple methodology:

take something in your left hand, take nothing in your right hand. Raise your hands.

Now say you are investigating a crime, and you know the crime weapon is in your hands.

What would be your conclusion?

 

Hello Michel123456,

 

I remember, your Allegory hit straight to my heart, the last time.

 

Will you please be more descriptive in the portrayal of the above.

 

 

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

 

I had assumed you were speaking of space as a shorthand for spacetime

 

Space ≠ spacetime

 

Spacetime is what is "bent". That is, the geometry of space and time that applies to phenomena is not the same near massive objects as it is far away from them.

I would like to transport two more posts here, for comparison with the above post, one from another thread & the other, an earlier post from this thread.

 

. . . Space-time is static. Nothing moves through it. The spacetime manifold embodies all of space and all of time -- past, present and future. Movement of a body is reflected in the world line of that body, which is a curve in the spacetime manifold. It can roughly be said that the body moves through "space" but not through spacetime. Even that requires a bit of thought as there is no such thing as a global notion of "space" (nor of "time"), and you need to understand the real meaning of local charts (What physicists call coordinates) . . .

--------------------------------------------&

Here is an excerpt from a book I am writing on relativity which discusses your question. Hope it helps:

For special relativity, Einstein came to embrace the notion that nothing exists beyond what we observe, what we can measure. He defined time as simply "what you read on a clock", and space as simply "the distance you measure between two points". The notion of time and space as anything beyond these "operational" definitions were, according to Einstein, simply the creation of the human mind.

In other words, time is relative; how fast it passes depends on the motion of the observer. This is measurable. However, the concept of time we hold in our minds is merely an abstraction. Einstein applied a similar view to "space".

 

But how can space contract? And how can the apparently same space contract differently for two (or more) observers in relative motion? Here Einstein is saying there is no "space" per se; only the distance between two points. The distance between the two points is measurable, albeit differently by the two observers. But "space" itself is again a mere abstraction.

 

In summary, we must "stop thinking about 'space and time' (as) something that is 'given to us', and must instead think about 'measuring positions and times', which is something we can do," writes Morton Tavel, professor of physics at Vassar College. "Only our measurements have real existence. We build up an intuition of something called space and time, which we believe exists beyond these measurements . . . (But) Einstein's first commandment was to pay attention only to your measurements and worry later about the properties of the more abstract notion of space and time." (My italics.)

 

Perhaps you find this approach to reality quite difficult to accept. So do I. Whether it is the years of thinking a certain way, or a particular bias of the human mind; I find it hard to accept that time and space are not real entities in their own right. But in special relativity, Einstein tells us that we must think of time and space as only the position on a clock and the markings on a ruler.

 

Einstein was to later develop a much broader view of space and time; first in considering the spacetime physics of his mathematics teacher, Hermann Minkowski, and most significantly, in his development of general relativity.

Ref: Victor J. Stenger, Quantum Gods, Creation, Chaos, and the Search for Cosmic Consciousness, p. 66.

J.A. Wheeler, A Journey into Gravity and Spacetime, p. 5

Morton Tavel, Contemporary Physics and the Limits of Knowledge (Rutgers, 2002), p. 58, as cited in Am. J. Phys. 74, 891 (2006).

 

Are these three posts indicating the same thing?

 

If so;

 

I had this following unresolved issue then,

 

and I repeat it here;

 

"From all the above three posts,

 

would it be proper to imply that;

 

The 'Space is a natural entity'.

 

However,

 

'Space-time' concerns the geometrical representation of an 'EVENT' occuring in that 'Space' or,

 

'Space-time' is a mathematical graph (or representation), of motion, of an object inside 'space'?"

 

And,

 

does this also mean that;

 

'Space-time' is an 'Abstract-Mathematical-Term', and does not represent an Entity or a System.

Edited December 10, 2011 by Anilkumar

[michel123456]

Will you please be more descriptive in the portrayal of the above.

It is my best description so far.

[Anilkumar]

I always stick to this very simple methodology:

take something in your left hand, take nothing in your right hand. Raise your hands.

Now say you are investigating a crime, and you know the crime weapon is in your hands.

What would be your conclusion?

 

Conclusion regarding what?

[michel123456]

Conclusion regarding what?

Where is the crime weapon, in the left or in the right hand?

[Anilkumar]

Where is the crime weapon, in the left or in the right hand?

 

I know that,

 

there is something else in my left hand and nothing in my right hand, then;

 

how would I convince myself that I have the crime weapon in my hand?

[Greg Boyles]

Hi everybody,

 

How and why does mass curve space?

 

Thank you.

 

 

Unless you are fairly gifted at mathematics, I am not, then the best way you could begin to understand this is through the classic two dimensional analogy where space time is represented by a sheet of elastic material.

 

If you then place a bowling ball on that elastic membrane it creates a dent in it it. If you then introduce a marble on to the membrane it creates a smaller dent. If the marble shoots past the dent caused by the bowling ball then it may have its coarse altered due it it travelling part the way around the curve of the dent. Or the marble may travel in a circle around the dent due to it having a slower initial velocity and passing by the bowling ball at a closer range so that it falls further down the dent. This latter example represents a smaller body going into orbit around a larger body.

 

 

Of course the analogy is far from perfect because friction between the solid bodies and the elastic suface would prevent the marble from truly orbiting the bowling ball, rather the marble would roll down the dent and hit the bowling ball.

[Anilkumar]

Unless you are fairly gifted at mathematics, I am not, then the best way you could begin to understand this is through the classic two dimensional analogy where space time is represented by a sheet of elastic material.

 

If you then place a bowling ball on that elastic membrane it creates a dent in it it. If you then introduce a marble on to the membrane it creates a smaller dent. If the marble shoots past the dent caused by the bowling ball then it may have its coarse altered due it it travelling part the way around the curve of the dent. Or the marble may travel in a circle around the dent due to it having a slower initial velocity and passing by the bowling ball at a closer range so that it falls further down the dent. This latter example represents a smaller body going into orbit around a larger body.

 

 

Of course the analogy is far from perfect because friction between the solid bodies and the elastic suface would prevent the marble from truly orbiting the bowling ball, rather the marble would roll down the dent and hit the bowling ball.

Thank you Greg Boyles,

 

for relating.

 

Though most of the analogy is amiable,

 

the hard part is,

 

assuming space time as a sheet of elastic material.

 

Now my perception of space is;

 

it is,

 

Structure-less, Empty & means Nothingness.

 

Then how to presume Nothingness as a material thing?

Edited December 11, 2011 by Anilkumar

[michel123456]

Unless you are fairly gifted at mathematics, I am not, then the best way you could begin to understand this is through the classic two dimensional analogy where space time is represented by a sheet of elastic material.

 

If you then place a bowling ball on that elastic membrane it creates a dent in it it. If you then introduce a marble on to the membrane it creates a smaller dent. If the marble shoots past the dent caused by the bowling ball then it may have its coarse altered due it it travelling part the way around the curve of the dent. Or the marble may travel in a circle around the dent due to it having a slower initial velocity and passing by the bowling ball at a closer range so that it falls further down the dent. This latter example represents a smaller body going into orbit around a larger body.

 

 

Of course the analogy is far from perfect because friction between the solid bodies and the elastic suface would prevent the marble from truly orbiting the bowling ball, rather the marble would roll down the dent and hit the bowling ball.

Anilkumar's question, and mine, is:

what is this grid made of?

If this grid is made of "nothing", then the analogy collapses.

My answer to this, through the left/right hand analogy above, is that knowing that the crime weapon is on your left

hand, you have to concentrate on what is in your left hand.

In the ball on the membrane analogy, the crime weapon, is not the grid, the crime weapon is the bowling ball.

IMHO the grid must be an emergent property of the bowling ball, not "something" in which matter stands.

 

Spacetime is not an entity that surrounds matter, it is an entity that exists inside matter as well. The grid is intricated inside the bowling ball. So much intricated that if you choose to represent spacetime as a 2D membrane, and if you want to remain coherent, you should represent the bowling ball as a flat disk.

 

It would become obvious that if spacetime changes shape where you put the ball, the ball should change shape as well and become curved.

And if we are observers inside the ball, then we would also change shape.

IOW gravity could be considered as a force that makes matter change shape.

Constantly.

IMHO of course.

[Greg Boyles]

Anilkumar's question, and mine, is:

what is this grid made of?

If this grid is made of "nothing", then the analogy collapses.

 

You are only asking that because we are in a 3 dimensional universe and you have the benefit of a god's eye view of this analogy.

 

In the real 3D situation the 'elastic fabric' is itself 3 dimendional, we are also 3 dimensional beings and we are trapped within that elastic fabric.

 

The 2D analogy is far from perfect because it involves 2D space time but 3D objects. Perhaps if the objects were heavy disks on the surface of the elastic fabric rather than spheres it would be a little clearer. Or perhaps if you had two eleastic membranes with heavy disks sandwiched between them.

 

And how do you know that our space is made of nothing? That is merely our perception of it. And as I understand it, string theory mathematics etc tells us that it may not be totally empty as we perceive it.

 

What about the neutrinos that are streaming out from the sun in vast quantities. They only interact very weakly with the matter that our bodies (and planets etc) are made of. So here alone the space between the Earth and the sun is far from empty and yet our senses give us no way of perceiving that fact.

 

It would become obvious that if spacetime changes shape where you put the ball, the ball should change shape as well and become curved.

And if we are observers inside the ball, then we would also change shape.

IOW gravity could be considered as a force that makes matter change shape.

Constantly.

Well they probably do but my understanding of the concepts is largely limited to the analogies which don't cover those sort of fine details.

Edited December 11, 2011 by Greg Boyles

[Anilkumar]

Anilkumar's question, and mine, is:

what is this grid made of?

If this grid is made of "nothing", then the analogy collapses.

My answer to this, through the left/right hand analogy above, is that knowing that the crime weapon is on your left

hand, you have to concentrate on what is in your left hand.

In the ball on the membrane analogy, the crime weapon, is not the grid, the crime weapon is the bowling ball.

IMHO the grid must be an emergent property of the bowling ball, not "something" in which matter stands.

 

Spacetime is not an entity that surrounds matter, it is an entity that exists inside matter as well. The grid is intricated inside the bowling ball. So much intricated that if you choose to represent spacetime as a 2D membrane, and if you want to remain coherent, you should represent the bowling ball as a flat disk.

 

It would become obvious that if spacetime changes shape where you put the ball, the ball should change shape as well and become curved.

And if we are observers inside the ball, then we would also change shape.

IOW gravity could be considered as a force that makes matter change shape.

Constantly.

IMHO of course.

 

Yes, Michel123456.

 

My thoughts are similar,

 

in regards to the grid & the Gravity.

 

That's what this thread is about.

 

 

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

 

. . . And how do you know that our space is made of nothing? That is merely our perception of it . . .

 

Does Physics hold this opinion?

Edited December 11, 2011 by Anilkumar

[URAIN]

Thanks Quenter,

 

for your concern.

 

 

 

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

 

one cannot act on 'NOTHING' ;

 

SPACE is 'NOTHING' ;

 

 

 

Anilkumar, Please dont call the space as nothing. According to P.P.Principle 'nothing' is only that, which has never existed in any time. i.e in past, in present and in future.

 

Other than this nothing, everything is the existence.

 

You may see this theory at www.baseforreincarnation.wordpress.com

 

 

 

[Anilkumar]

Anilkumar, Please dont call the space as nothing. According to P.P.Principle 'nothing' is only that, which has never existed in any time. i.e in past, in present and in future.

 

Other than this nothing, everything is the existence.

 

You may see this theory at www.baseforreincarnation.wordpress.com

 

 

'Nothing' here, means, 'made up of nothing', i.e.

 

'Emptiness', 'Vacancy', 'Structure-less',

 

I did not mean 'Non-existant'.

 

Though I appreciate your concern;

 

(I had a glance through the links you suggested)

 

but,

 

at this point,

 

I am more interested in,

 

Spacetime curvature,

 

than Reincarnation.

 

Thank you.

Edits: Italics

Edited December 12, 2011 by Anilkumar