Time in Early Universe

[Bubblesofearth]

Just to add.

I think part of the problem may be that you are only used to thinking of curvature in terms of extrinsic curvature since that is what you see when looking at surfaces within our universe from the outside - so for instance you are used to seeing a cylinder as being curved whereas its intrinsic curvature is flat.

Leaving aside the question of an embedding space doesn't the intrinsic curvature of space-time imply the need for a 4th dimension? If so do we have any knowledge of this?

BoE

[ursaminortaur]

Just to add.

I think part of the problem may be that you are only used to thinking of curvature in terms of extrinsic curvature since that is what you see when looking at surfaces within our universe from the outside - so for instance you are used to seeing a cylinder as being curved whereas its intrinsic curvature is flat.

Leaving aside the question of an embedding space doesn't the intrinsic curvature of space-time imply the need for a 4th dimension? If so do we have any knowledge of this?

BoE

Mathematically intrinsic curvature only depends on the internal properties of the surface which by definition has the dimensionality of that surface and hence does not require any reference to a higher dimension. Hence the intrinsic curvature of our 3d universe does not require the existence of a 4th spatial dimension.

[Bubblesofearth]

Mathematically intrinsic curvature only depends on the internal properties of the surface which by definition has the dimensionality of that surface and hence does not require any reference to a higher dimension. Hence the intrinsic curvature of our 3d universe does not require the existence of a 4th spatial dimension.

I've tried reading around this but suspect I lack the maths and physics to properly understand it. AFAICS;

Time moves more slowly when gravity is higher.

Light will pass from points A to B along a path of shortest time.

So does this mean that the bending of light as it passes a massive body is due to the shortest time being a partial avoidance of the gravitational field of the body?

I realise I'm off on a bit of a tangent here but just trying to get a sense of what is going on.

BoE

[odysseus2000]

Mathematically intrinsic curvature only depends on the internal properties of the surface which by definition has the dimensionality of that surface and hence does not require any reference to a higher dimension. Hence the intrinsic curvature of our 3d universe does not require the existence of a 4th spatial dimension.

I've tried reading around this but suspect I lack the maths and physics to properly understand it. AFAICS;

Time moves more slowly when gravity is higher.

Light will pass from points A to B along a path of shortest time.

So does this mean that the bending of light as it passes a massive body is due to the shortest time being a partial avoidance of the gravitational field of the body?

I realise I'm off on a bit of a tangent here but just trying to get a sense of what is going on.

BoE

A simple way of thinking is to note that the effect of mass is to distort space and as light travels in space, it is also deflected. A simple idea of the distortion is seen in the second image down, right hand side:

https://en.wikipedia.org/wiki/Gravitational_lens

The 3rd image (animation) shows the ring effect of a light source with a large mass passing in front of it and seen by an observer a long way off directly in line with the mass and the light source beyond the mass.

The phenomena has been experimentally demonstrated and it is now a well established observational approach with techniques including radio astronomy where sub arc second resolution is achieved.

The whole wiki page on gravitational lensing is well worth reading. It is amazing, at least to me, that Newton came to the conclusion that mass would
bend light.

Regards,

[ursaminortaur]

Mathematically intrinsic curvature only depends on the internal properties of the surface which by definition has the dimensionality of that surface and hence does not require any reference to a higher dimension. Hence the intrinsic curvature of our 3d universe does not require the existence of a 4th spatial dimension.

I've tried reading around this but suspect I lack the maths and physics to properly understand it. AFAICS;

Time moves more slowly when gravity is higher.

Light will pass from points A to B along a path of shortest time.

So does this mean that the bending of light as it passes a massive body is due to the shortest time being a partial avoidance of the gravitational field of the body?

I realise I'm off on a bit of a tangent here but just trying to get a sense of what is going on.

BoE

Light follows a geodesic which is the equivalent of a straight line in euclidean space and is the shortest path. In general relativity mass distorts both time and space in its vicinity which results in that space having greater intrinsic curvature in that region. This means that the geodesic can curve around the mass.

Your explanation of

a partial avoidance of the gravitational field of the body

sounds to me like you are suggesting that the light beam is bent away from the mass into an area with less gravity. Whereas what actually happens is that the light is bent closer to the mass. Even though photons have no rest mass they are pulled towards a mass just as particles with mass are pulled towards a massive object by the attraction of gravity.

See

https://nasa.tumblr.com/post/187009797389/how-gravity-warps-light

And note in the examples that the beams of light that are bent and reach the observer would have missed the observer completely if there was no intervening mass and are bent back towards that mass on their way to the observer.

[odysseus2000]

Just a brief point.

Photons are assumed massless but they carry momentum (p), expressed as energy (e) =p*c where c is the velocity of light, whereas a particle with mass has an additional term e**2 =p**2c**2 + m0**2c**4.

Until relatively recently neutrino were also thought massless, but there was a small time delay in the observation of neutrino compared to other observable from the supernova 1987a giving a hint that neutrino had mass and this was confirmed by Super Kamiokande and the Sudbury Solar Neutrino observatory which confirmed the earlier results of Davis in the North Dakota gold mine with two Nobel prizes being won spread across these groups.

Some theories suggest photons too have tiny mass. The limit on the mass of a photon is now 10**-48 Kg:

https://www.science.org/content/article ... %20photons.

Regards,