Could gravity be described as distance compression?

[kwerk]

Two people leave from parallel points in space and head to other parallel points the same distance apart.

Person 1 travels through empty space outside any gravitational influence, and it takes him 1 day to reach his destination.

Person 2 comes close to a black hole on the way. It takes him 10 years to reach his destination. The overall distance in space is the same but person 2 has actually traveled much further, because he traveled through a compressed area of space.

Could you say the black hole is compressing distance? Does that make any sense as an idea, that space time isn't bent by gravity but simply distance is compressed? That you are not actually measuring time, but distance relative to other distance? Time has not slowed in the black hole but distance has been compressed.

 

[Q-reeus]

Two people leave from parallel points in space and head to other parallel points the same distance apart.

Person 1 travels through empty space outside any gravitational influence, and it takes him 1 day to reach his destination.

Person 2 comes close to a black hole on the way. It takes him 10 years to reach his destination. The overall distance in space is the same but person 2 has actually traveled much further, because he traveled through a compressed area of space.

Could you say the black hole is compressing distance? Does that make any sense as an idea, that space time isn't bent by gravity but simply distance is compressed? That you are not actually measuring time, but distance relative to other distance? Time has not slowed in the black hole but distance has been compressed.

How would you then be able to explain gravitational redshift? http://en.wikipedia.org/wiki/Gravitational_redshift"

 

[HallsofIvy]

The fact that you think "parallel points" is a meaningful phrase makes me wonder how much of any respose you would understand,.

 

[kwerk]

What I mean is two routes the same distance in overall space. Like two routes on Earth when looking down from above, except one route goes over a hill. You can't see the hill when looking at the 2D route. They are going the same distance but one guy has to go over the hill so is really traveling further. When you look from above it would seem like the distance has been compressed where he hits the hill. From above it would look like time has slowed down for him as he walks up and down the big hill.

 

[Q-reeus]

What I mean is two routes the same distance in overall space. Like two routes on Earth when looking down from above, except one route goes over a hill. You can't see the hill when looking at the 2D route. They are going the same distance but one guy has to go over the hill so is really traveling further. When you look from above it would seem like the distance has been compressed where he hits the hill. From above it would look like time has slowed down for him as he walks up and down the big hill.

Gravity effects both time and distance. While distance does compress so to speak near a gravitating mass (but only the radial component according to the standard Schwarzschild metric: http://en.wikipedia.org/wiki/Schwarzschild_metric), time also and always slows (relative to a distant observer). That's what gravitational redshift (link in #2) really means - clocks closer to the mass tick slower relative to an identical clock further out. This article may help: http://en.wikipedia.org/wiki/Gravitational_time_dilation

 

[kwerk]

Yes the clock would be ticking slower, but has time really slowed down or is the hand of the clock just moving a further distance through compressed space than the other clock? Right down to electrons and stuff, could they simply be traveling a further distance through compressed space but appear to be slowed down in time? The medium they are traveling through (empty space) has become denser, but in a way we can't really observe?

 

[Q-reeus]

Suppose we take distance only to have compressed - the clock merely shrinks in size wrt someone further out. It would take the same time for the hands to complete one revolution, they would merely sweep out a smaller circle. A genuine slowing of time can only mean the hands also take longer to complete one revolution. Gravitational redshift can be considered then as the light source, further in, likewise vibrating at a slower rate (I should add this is a consistent interpretation, but some think in terms of energy loss in climbing out of the gravitational well). Convert that into say a vehicle traveling along your highway. It will be traveling slower from the combined effects of smaller wheels (the distance part), and slower rpm (the time part). Shapiro time delay for a light beam takes both effects into account, and has now been confirmed to very high accuracy:
http://en.wikipedia.org/wiki/Tests_of_general_relativity#Light_travel_time_delay_testing

 

[yuiop]

There is a slight problem with parallel lines when a black hole is nearby because the curvature of space means that the lines will not be straight in the classical sense and any geodesic path passing close to a black hole will be curved.

Here is a slight modification to your thought experiment to try and circumvent that difficulty. Let us say we have two very large rings. One ring has a large neutron star at its centre and the other is very far away from any gravitational sources. We directly measure the circumferences of the two rings (independently of radial measurements) and agree they are equal. The neutron star conveniently has a tunnel drilled through its centre. Now we lay very short rulers along the diameter of the rings. These rulers are calibrated using radar measurements and if we bring any two rulers alongside each other we agree they are the same length. We find we need more rulers to span the diameter of the ring that contains the neutron star. In this sense, yes, you can say that in a way the distance is compressed in the ring with the gravitational source, if you like that visualisation. In a loose interpretation, you could possibly say the traveller that passes through the neutron star travels a further distance than the other traveller in the empty ring, in the same coordinate time and so he must have had a greater average velocity and therefore experienced a greater velocity related time dilation. However, as others here have pointed out, there is an additional time dilation factor due to gravity, on top of the velocity related time dilation, that is experienced even if the the observer has zero velocity in the gravitational field, so gravitational time dilation can not be explained by apparent compression of distances.