Visualising curved space

[xelasnave]

I found this thread very interesting.

It seems silly for me to offer a comment given my lack of grip on the concept space time... I realise there are specific math implications... however the question was...........

"Has anyone managed to find a mental trick to assist in visualising a curved space?"

So I offer how I "see" space in a geometric visualisation..up and down to me are irrelevant so the problem with the ant is lost on me...

Still I feel space can be looked at like a barometric map..but in 3d.. start with a visualisation of a 3d grid...make the cubes any size... but all the same size..this is unbent space... as you get closer to mass the grid becomes smaller...making greater gravity in effect...but as everything is moving none of the grid lines remain straight and across the expanses of space would probably resemble more smoke drifting in a light breeze... the complexity of the various curvatures would see one having trouble then holding to a regular grid but one that is distorted greatly...

Also for who ever can field this one....IF Earth does not curve space how does GR give us our gravity???

alex
alex

[sjastro]

Originally Posted by xelasnave

Also for who ever can field this one....IF Earth does not curve space how does GR give us our gravity???

alex
alex

Good question Alex.

In the absence of mass (and gravity), space is perfectly flat.

The strength of the gravitational field as a function of mass density determines the degree of space time curving.

The Earth's field strength is not strong enough for any significant space time curving.

It's no coincidence that for weak gravitational fields GR equations reduce to Newtonian equations. Hence Newtonian physics becomes a very good approximation for GR for weak fields.

Steven

[Archy (George)]

Originally Posted by sjastro

By mentioning the planet Earth I have automatically defined.

(a) It's mass
(b) It's diameter (or volume)

The statement "Since the Earth is not sufficently massive to cause space-time to curve.... " should therefore be self evident.

In other words the Earth is not sufficently massive for it's diameter (or volume) to cause space time to curve.

Density=mass/volume. If volume is constant, then density is purely a function of mass. Increasing mass increases the density which may cause space time to curve.

Hence there is no contradiction.



Neutron stars have solar masses around 1.3 -2.1 where as the progenitor stars before becoming supernovas are 15 solar masses or more.

Neutron stars can form gravitational lens due to space time curving. 15 solar mass stars do not. This is because the density of Neutron stars is very much greater.

Steven

Not to the point: the contradiction in your statements are self evident

[Archy (George)]

Originally Posted by sjastro

Neutron stars have solar masses around 1.3 -2.1 where as the progenitor stars before becoming supernovas are 15 solar masses or more.

Neutron stars can form gravitational lens due to space time curving. 15 solar mass stars do not. This is because the density of Neutron stars is very much greater.

Steven

Sure, I don't ague that mass doesn't affect space-time, I ask again how does it effect space-time.

[Archy (George)]

Originally Posted by sjastro

The statement "Since the Earth is not sufficently massive to cause space-time to curve.... " should therefore be self evident.

In other words the Earth is not sufficently massive for it's diameter (or volume) to cause space time to curve.

Steven

The Earth is massive enough to curve space-time: if it were not, there would be no gravity.
Since we do experience gravity, my first statement "We all live in curved space so we don't notice it" has to be modified to:
We all live in curved space time and experience it as gravity.

[sjastro]

Originally Posted by Archy

The Earth is massive enough to curve space-time: if it were not, there would be no gravity.

Since we do experience gravity, my first statement "We all live in curved space so we don't notice it" has to be modified to:
We all live in curved space time and experience it as gravity.

Ever heard of Einstein's principle of equivalence on which GR is founded? Evidently not.

We experience gravity in the gravitational field.
We can also experience the same gravity by being accelerated at g in a gravity free field. A gravity free field is flat space.

Hence we can experience gravity in flat space which contradicts your post.

It is how curved space time acts on bodies and light that would otherwise be travelling in a straight line in flat space that reveals it's presence.

As mentioned in a previous thread the perhelion advance of a planet is one way. The advance of the moons orbit is explained by classical means (ie tides) and is not due to space time curving.

The Earth's field is not strong enough for the effects of space time curving
to be observed.
The moons orbit is satisfactorily explained by Newtonian physics.

They are the facts!

On a final note this is my last response to your posts. It's quite obvious where this thread is heading.

[Archy (George)]

Originally Posted by sjastro

Ever heard of Einstein's principle of equivalence on which GR is founded? Evidently not.

We experience gravity in the gravitational field.
We can also experience the same gravity by being accelerated at g in a gravity free field. A gravity free field is flat space.

Hence we can experience gravity in flat space which contradicts your post.

It is how curved space time acts on bodies and light that would otherwise be travelling in a straight line in flat space that reveals it's presence.

As mentioned in a previous thread the perhelion advance of a planet is one way. The advance of the moons orbit is explained by classical means (ie tides) and is not due to space time curving.

The Earth's field is not strong enough for the effects of space time curving
to be observed.
The moons orbit is satisfactorily explained by Newtonian physics.

They are the facts!

On a final note this is my last response to your posts. It's quite obvious where this thread is heading.

Re: "Ever heard of Einstein's principle of equivalence on which GR is founded": Yes I have: the Wikipedia says: "In the physics of relativity, the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference."
It might be noted that it is apparent from your posts in this thread that you do not agree with Wikipedia that the Earth is a massive body.

Re: "We experience gravity in the gravitational field.
We can also experience the same gravity by being accelerated at g in a gravity free field. A gravity free field is flat space.

Hence we can experience gravity in flat space which contradicts your post."

The last two statements are contradictory.

Re: "The Earth's field is not strong enough for the effects of space time curving
to be observed." Is incorrect: the GPS system has a correction algorithm to correct for changes in space-time.

[Archy (George)]

To Steven
On a final note: You say space-time is affected by density, that the earth does not curve space-time and, I infer, that the precession of mercury shows the sun's effect on space-time.
How can you explain these views when the sun's density is 1.4 g/cm3 (Namowitz, Samuel N. Heath Earth Science. Canada: Heath, 1994: 379. "… Sun's density is 1.4 times that of water.)
and the Earth's density is 5.519 g/cm3 (Neff, Robert F. & Zitewitz, Paul W. Physics, Principles and Problems. New York: Glencoe, 1995: 159. "Mass of the Earth 5.979 × 1024 kg Radius of the Earth 6.3713 × 103 km)

The sun curves space-times more than the earth because it is more massive, not because it is denser.

[sjastro]

Originally Posted by Archy

Re: "Ever heard of Einstein's principle of equivalence on which GR is founded": Yes I have: the Wikipedia says: "In the physics of relativity, the equivalence principle refers to several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference."
It might be noted that it is apparent from your posts in this thread that you do not agree with Wikipedia that the Earth is a massive body.


Re: "We experience gravity in the gravitational field.
We can also experience the same gravity by being accelerated at g in a gravity free field. A gravity free field is flat space.

Hence we can experience gravity in flat space which contradicts your post."

The last two statements are contradictory.

A non inertial frame of reference is accelerated in gravity free space.
The pseudo force is your gravity.
It simply confirms that the effects of gravity can occur in flat space for the reasons I have already given.

Re: "The Earth's field is not strong enough for the effects of space time curving
to be observed." Is incorrect: the GPS system has a correction algorithm to correct for changes in space-time.

Changes to space-time doesn't make any sense.

Corrections to GPS systems involve the synchronization of Earth clocks and GPS satellite clocks.

GR predicts a clock at a higher gravitational potential (ie a clock on the Earths surface) will run slower than one at a lower potential (satellite clock).

This is an example of gravitational red shift which has nothing to do with the geometry of space-time. In fact the original concept of gravitational red shift was devised using SR which assumes that space is flat.

[sjastro]

Originally Posted by Archy

To Steven
On a final note: You say space-time is affected by density, that the earth does not curve space-time and, I infer, that the precession of mercury shows the sun's effect on space-time.
How can you explain these views when the sun's density is 1.4 g/cm3 (Namowitz, Samuel N. Heath Earth Science. Canada: Heath, 1994: 379. "… Sun's density is 1.4 times that of water.)
and the Earth's density is 5.519 g/cm3 (Neff, Robert F. & Zitewitz, Paul W. Physics, Principles and Problems. New York: Glencoe, 1995: 159. "Mass of the Earth 5.979 × 1024 kg Radius of the Earth 6.3713 × 103 km)

The sun curves space-times more than the earth because it is more massive, not because it is denser.

The answer is obvious.
The Sun's density of 1.4 g/cm3 is an average density.

The density of the core is 150 g/cm3 which is why space time curves at the Sun. It has nothing to do with mass.

Stars of 15 solar masses or more require the thermonuclear reactions to keep their cores from collapsing under gravity.

If the core does collapse a supernova occurs and the core forms a super dense neutron star or black hole with the corresponding space time curvature.

The mass of a neutron star is much less than the original star but the density is millions of times greater than the average density of the original star.

[Archy (George)]

Originally Posted by sjastro

A non inertial frame of reference is accelerated in gravity free space.
The pseudo force is your gravity.
It simply confirms that the effects of gravity can occur in flat space for the reasons I have already given.



Changes to space-time doesn't make any sense.

Corrections to GPS systems involve the synchronization of Earth clocks and GPS satellite clocks.

GR predicts a clock at a higher gravitational potential (ie a clock on the Earths surface) will run slower than one at a lower potential (satellite clock).

This is an example of gravitational red shift which has nothing to do with the geometry of space-time. In fact the original concept of gravitational red shift was devised using SR which assumes that space is flat.

1. An acceleration produces a real force, not a pseudo force.
2. Mass distorts space see: Slide 17 http://www.physics.ucsd.edu/~tmurphy...15_gen_rel.ppt. from which we see the statement "Mass tells space-time how to curve and Space tells mass how to move....Gravity is a property of the geometry of spacetime"
3. Since frequency is a function of inverse time (eg beats per second) a change in frequency, which is what is implied by a redshift, requires a change in time (since there are the same number of beats), which agrees with what I have said that the mass of the earth causes a change in space-time
4. Re the GPS see: Pogge, Richard W., “Real-World Relativity: The GPS Navigation System” where in the seventh para graph there is the statement:
   "Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day." (Bold and underlining are mine.)

You, of course, are free to believe that the earth does not distort spacetime because it is not dense enough, or whatever else you wish.

[sjastro]

Originally Posted by Archy

An acceleration produces a real force, not a pseudo force.

You change the subject matter when it's convenient for you.
This has nothing to do with the context of the equivalence principle.

"All fictitious forces are proportional to the mass of the object upon which they act, which is also true for gravity.[17] This led Albert Einstein to wonder whether gravity was a fictitious force as well. He noted that a freefalling observer in a closed box would not be able to detect the force of gravity; hence, freefalling reference frames are equivalent to an inertial reference frame (the equivalence principle). Following up on this insight, Einstein was able to formulate a theory with gravity as a fictitious force; attributing the apparent acceleration of gravity to the curvature of spacetime. This idea underlies Einstein's theory of general relativity."

Mass distorts space see: Slide 17 www.physics.ucsd.edu/~tmurphy/phys10/lectures/15_gen_rel.ppt. from which we see the statement "Mass tells space-time how to curve and Space tells mass how to move....Gravity is a property of the geometry of spacetime"

And what do you think is the property of mass that causes this, it is density. It's why low mass high density Neutron stars cause space time to distort.

Since frequency is a function of inverse time (eg beats per second) a change in frequency, which is what is implied by a redshift, requires a change in time (since there are the same number of beats), which agrees with what I have said that the mass of the earth causes a change in space-time

You haven't explained anything. There is no relationship between frequency and geometry.

Re the GPS see

: Pogge, Richard W., “Real-World Relativity: The GPS Navigation System” where in the seventh para graph there is the statement:


"Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day." (Bold and underlining are mine.)

Red shift (or time dilation due to gravity) is independant of space time geometry. It can occur in flat space or curved space and is dependant on the gravitational potential differences between earth and satellite clocks.

As I have already mentioned gravitational redshift has been mathematically formulated using flat space (and the equivalence principle).

You, of course, are free to believe that the earth does not distort spacetime because it is not dense enough, or whatever else you wish.

I certainly did not state the Earth does not distort space time, but on the basis of observation the effects are not apparent.
And on that note this thread is concluded.

[Jay-qu]

For anyone wanting an actual visualisation of curved space here are some links with videos created by my General relativity lecturer at uni:

http://users.monash.edu.au/~leo/rese.../gr/index.html
http://users.monash.edu.au/~leo/rese.../sr/index.html

[Archy (George)]

Originally Posted by sjastro

You change the subject matter when it's convenient for you.
This has nothing to do with the context of the equivalence principle.

"All fictitious forces are proportional to the mass of the object upon which they act, which is also true for gravity.[17] This led Albert Einstein to wonder whether gravity was a fictitious force as well. He noted that a freefalling observer in a closed box would not be able to detect the force of gravity; hence, freefalling reference frames are equivalent to an inertial reference frame (the equivalence principle). Following up on this insight, Einstein was able to formulate a theory with gravity as a fictitious force; attributing the apparent acceleration of gravity to the curvature of spacetime. This idea underlies Einstein's theory of general relativity."




And what do you think is the property of mass that causes this, it is density. It's why low mass high density Neutron stars cause space time to distort.



You haven't explained anything. There is no relationship between frequency and geometry.



Red shift (or time dilation due to gravity) is independant of space time geometry. It can occur in flat space or curved space and is dependant on the gravitational potential differences between earth and satellite clocks.

As I have already mentioned gravitational redshift has been mathematically formulated using flat space (and the equivalence principle).




I certainly did not state the Earth does not distort space time, but on the basis of observation the effects are not apparent.
And on that note this thread is concluded.

Rubbish: I have stayed on the subject.
If you think gravity is fictitious: go jump off a tall building.

Density is not a property of mass, but mass is a property of density.
Where do you get the idea that a neutron star has low mass: according to NASA a neutron star has the mass of about 1.4 times that of our Sun.
Despite what you have asserted, the Earth does change the geometry of space-time. Certainly not to the extent of a neutron star, nor to the extent that our sun does, but nevertheless by a measurable and measured amount as I have already illustrated.

Get off: who are you to say the thread is concluded

[xelasnave]

Will the Gravity B probe mission show curvature or is it limited to showing frame dragging? and I cant recall the variance they look for to demonstrate framedragging but I do remember it being a very small number they expected to be working with... I had all this on my dead lappy but without it I can not be more specific unless I read the available material from the net...however one would think one could not show frame dragging unless you did not have a demonstratable curvature of space.

This is a wonderful thread please dont end it too early.
We must remember that strangly the subject of gravity can get folk going.. one would not think this could be the case but it has been my experience... and so we proceed knowing the subject can be as volitile as religion or politics.. and I am not sure that gravity is entirely issolated from either of those considerations.

alex

[sjastro]

Originally Posted by xelasnave

Will the Gravity B probe mission show curvature or is it limited to showing frame dragging? and I cant recall the variance they look for to demonstrate framedragging but I do remember it being a very small number they expected to be working with... I had all this on my dead lappy but without it I can not be more specific unless I read the available material from the net...however one would think one could not show frame dragging unless you did not have a demonstratable curvature of space.

Alex,

The gravity B probe will measure the geodetic effect (space-time curvature) and frame dragging.

The geodesic effect is one part in 10000 deviation from flat space.
The frame dragging effect is one part in a few trillion.

Putting the geodesic effect in perpsective, it doesn't require us to jettison Newtonian mechanics, space around Earth is still essentially flat.

This is a wonderful thread please dont end it too early.

I'm no longer contributing to the thread that shouldn't stop anyone else.

Regards

Steven

[xelasnave]

Thank you for your reply Steven
alex

[Archy (George)]

Originally Posted by xelasnave

Will the Gravity B probe mission show curvature or is it limited to showing frame dragging? and I cant recall the variance they look for to demonstrate framedragging but I do remember it being a very small number they expected to be working with... I had all this on my dead lappy but without it I can not be more specific unless I read the available material from the net...however one would think one could not show frame dragging unless you did not have a demonstratable curvature of space.

This is a wonderful thread please dont end it too early.
We must remember that strangly the subject of gravity can get folk going.. one would not think this could be the case but it has been my experience... and so we proceed knowing the subject can be as volitile as religion or politics.. and I am not sure that gravity is entirely issolated from either of those considerations.

alex

This link may be of use re frame dragging: http://www.nasa.gov/vision/earth/loo...arth_drag.html

[xelasnave]

Thanks for the link George
alex