Can time be compressed without affecting distance?

[LordChallen]

In tune with the idea that gravity can affect time, can gravity affect distance?

Like, if I am traveling a specific velocity I can reach a place in a specific amount of time. But if time is compressed, relative a remote observer, I would reach my destination sooner.

But, if you pull a measuring tape from point to point, it should remain unaffected.

TIA

 

[FactChecker]

Gravity distorts both time and space. Straight lines are no longer the same, so distances are different.

 

[LordChallen]

But how do we know which is being distorted and by how much? For example, if hypothetically, I put a 25-foot tape through a 20-foot time dilation bubble would it change the distance to the other side?

Obviously I could measure the outside of the time dilation bubble and it would still be 20 feet. But what would happen to the measuring tape that I stuck through it?

A black hole may cause time to slow to almost a stopping point. But what happens to distance? Is that black hole bigger on the inside?

Gravity can bend light but can it change the speed of it?

 

[Nugatory]

But how do we know which is being distorted and by how much?

We don't. We know what the curvature of spacetime is, but how we divide that up into curvature of time and curvature of space is pretty much arbitrary. For a easier example from flat spacetime (no curvature or gravitational effects important enough to matter) consider observations of muons produced by cosmic rays (there's a pretty decent overview here: http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html). We can choose to think of the problem as if the Earth is at rest and the muons are moving towards it at relativistic speed; because the muons are moving, time dilation means that the muons live longer so travel farther through the atmosphere before they decay. But we can also think of the problem as if the muon is at rest and the Earth is rushing towards; there's no time dilation to extend the life of the muon because it as rest, but the distance from the top of the atmosphere to the surface of the Earth is length contracted so the muon doesn't have as far to go and still reaches the Earth before it decays. Both perspectives are equally valid; they're just different descriptions of the same physical process.

But what happens to distance? Is that black hole bigger on the inside?

We don't need a black hole for that question - any gravitating body will do. If the Earth were a perfect sphere we would expect that the disatnce through the center would be related to its circumference by $C=2\pi{d}$, but it's not - the distance is very slightly larger, and you could interpret that as saying that it is "bigger inside".

Gravity can bend light but can it change the speed of it?

No, the speed of light is always $c$ if you measure the speed of a flash zipping by you. But you need to be very very careful about what you're calling the speed of anything, including light, if it's moving between two distant points instead of zipping by you.

 

[LordChallen]

All things being relative,

Velocity = Distance/Time.

If a gravity center slows time, wouldn't the distance have to increase for this rule to be true?

Like, if you fell into a black hole, time would slow as you approached. But you might never actually get to the black hole because the distance would increase as time slowed.

To outside observer, the distance would be short, but the time long. To an inside observer, time would remain constant by the distance would increase.

When a comet approaches the Sun, it spreads it tail out behind. Now, as far as I know, people say this is because of dust and gas coming off the object. But would gravity pull equally all everything? And as the comet departs, would sun's gravity try to pull dust and gases back? Instead, the dirt and gas caught up to the comet.

What if, the size of comet, was enough to response to micro-layers of changes in time? So the front of the comet might react a micro-second fast then the back of comet. Over billions of miles, this effect would have the comet stretched over thousands of miles. At the comet departed, the effect would reverse and the parts could collect again. The appearance of the comet gaining speed could time compressing, while inside the time/space might remain constant.

 

[PeterDonis]

Velocity = Distance/Time.

If a gravity center slows time, wouldn't the distance have to increase for this rule to be true?

You seem to think that Velocity = Distance/Time is a law of physics. It's not. It's just a definition.

if you fell into a black hole, time would slow as you approached

That depends on how you compare your "rate of time flow" to someone else's. There is no unique way to do that.

you might never actually get to the black hole because the distance would increase as time slowed

You don't have to speculate. You can compute the answer using the laws of physics: the Schwarzschild solution to the Einstein Field Equation, in this case. The answer is that you can indeed fall into a black hole. The laws also tell us that the distance you have to fall does not change as you fall.

 

[LordChallen]

In another thread, someone hypothetically suggested that a spaceship orbiting Earth at the speed of light for 1 years (relative to the spaceship) would be 7000 years relative to people observers on earth. Even though the spaceship only when 1 light year, to Earth observers, 7000 light years.

The actually distance covered is 7000x more then expected for the spaceship. So distance does expand as time shrinks?

So in theory, an expanding universe could be shrinking time?

 

[PeterDonis]

In another thread,

Link please?

someone hypothetically suggested that a spaceship orbiting Earth at the speed of light for 1 years (relative to the spaceship) would be 7000 years relative to people observers on earth. Even though the spaceship only when 1 light year, to Earth observers, 7000 light years

Yes, due to time dilation. Also, the spaceship can't travel at the speed of light. It can only travel close to the speed of light, relative to Earth. You should be able to calculate how close to the speed of light it would have to travel in order to have a time dilation factor, relative to Earth, of 7000 to 1.

Furthermore, in such a calculation, the effect of the Earth's gravity on time is negligible. It is many orders of magnitude smaller than the 7000 to 1 ratio.

The actually distance covered is 7000x more then expected for the spaceship

The distance covered by the spaceship, in the Earth frame, is just whatever distance is covered by however many orbits the spaceship makes in 7000 Earth years.

The gravity of the Earth has negligible effect on this distance. The motion of the spaceship relative to Earth has no effect on it at all (except that the ship's speed determines how many orbits it makes in 7000 Earth years).

The spaceship's motion is not inertial, so there is no way to construct an inertial frame in which it is at rest. So there is no obvious frame in which the Earth is moving and covers a distance 7000x less, relative to the spaceship, than the distance the spaceship covers, relative to the Earth, in the Earth frame. But even if we could construct such a frame, the length contraction in this frame would have nothing to do with Earth's gravity.

So distance does expand as time shrinks?

No. Even in SR, distances in moving frames contract; they don't expand.

So in theory, an expanding universe could be shrinking time?

No.

 

[PeterDonis]

The thread topic has been sufficiently addressed. Thread closed.