I Gravity Inside and Outside a Moving Lift

[Sandeep T S]

Yesterday I post a thread, this post is continue of that one.
In pic 1 lift is accelerating. A observe inside the lift would assume that he is on planet. if he is on planet time slow on ground and fast in sky. Pic2 shows gravitational field, that have high magnitude in bottom, low at top.
Assume a window on the lift , we open that in pic3 the observer realize he is not on the planet. But what happened to the field we had drawn, is it instantaneously changed?

 

[Nugatory]

When the window is opened the gravitational effects don't change and the time dilation (clock at bottom runs slow compared with the clock at the top) doesn't change. The only thing that does change is the observer's explanation of why these things are happening.

 

[Sandeep T S]

When the window is opened the gravitational effects don't change and the time dilation (clock at bottom runs slow compared with the clock at the top) doesn't change. The only thing that does change is the observer's explanation of why these things are happening.

Do you mean that if I knew that, I am accelerating. Then the bottom field and top field are not equal, I am I right

 

[Nugatory]

Do u mean that if I knew that, I am accelerating. Then the bottom field and top field are not equal, I am I right

No. I mean that everything that happens inside the lift (clocks at the bottom run slow compared with clocks near the top, dropped objects accelerate towards the floor) is the same whether the lift is sitting still in a uniform gravitational field or accelerating through space. This is the equivalence principle.

Opening the window and looking outside just let's us say "Oh, I see that we're sitting still on the ground - these things must be happening because of the Earth's gravity" or "Oh, I see that we're accelerating through empty space and that's why these things are happening inside the lift". The only thing that changes because we've opened the window is that we know what's happening outside the lift as well as inside.

 

[Sandeep T S]

Oh ,principle of equivalence postulate that a accelerating thing have proparty of gravitation field

 

[Sandeep T S]

Is observer out side lift also figure the time dilation on bottom and top

 

[Nugatory]

Is observer out side lift also figure the time dilation on bottom and top

Suppose that the two clocks are identically constructed, so that if we put them side by side in the same place and at rest relative to one another both will tick at the same rate. Furthermore, suppose that the clocks are constructed so they emit a flash of light every time they tick.

Now, if we put one clock at the top of the lift and the other at the bottom, an observer next to either clock will see periodic flashes of light coming from the other clock.

Suppose a flash of light from the lower clock reaches the upper clock at the moment that the upper clock ticks. The next flash of light will reach the upper clock after its next tick; the upper clock is ticking fast compared with the lower clock. Conversely, if a flash of light from the upper clock reaches the lower clock at the same moment that the lower clock ticks, the next flash of light from the upper clock will reach the lower clock before its next tick, again showing that the upper clock is running fast compared with lower clock.

All observers everywhere will agree about these facts.

 

[Sandeep T S]

Suppose that the two clocks are identically constructed, so that if we put them side by side in the same place and at rest relative to one another both will tick at the same rate. Furthermore, suppose that the clocks are constructed so they emit a flash of light every time they tick.

Now, if we put one clock at the top of the lift and the other at the bottom, an observer next to either clock will see periodic flashes of light coming from the other clock.

Suppose a flash of light from the lower clock reaches the upper clock at the moment that the upper clock ticks. The next flash of light will reach the upper clock after its next tick; the upper clock is ticking fast compared with the lower clock. Conversely, if a flash of light from the upper clock reaches the lower clock at the same moment that the lower clock ticks, the next flash of light from the upper clock will reach the lower clock before its next tick, again showing that the upper clock is running fast compared with lower clock.

All observers everywhere will agree about these facts.

So there is a accelration gradient along its length

 

[jartsa]

So there is a accelration gradient along its length

You mean is there some thing in an accelerating rocket that affects clocks?

No there is not.

The person inside the rocket observes a field that affects clocks. That person inside the rocket is an accelerating observer, that is the reason for that observation. Non-accelerating observers do not observe any field.

 

[pervect]

Yesterday I post a thread, this post is continue of that one.
In pic 1 lift is accelerating. A observe inside the lift would assume that he is on planet. if he is on planet time slow on ground and fast in sky. Pic2 shows gravitational field, that have high magnitude in bottom, low at top.
Assume a window on the lift , we open that in pic3 the observer realize he is not on the planet. But what happened to the field we had drawn, is it instantaneously changed?View attachment 220794

Let's add something physical to your picture, a clock about half a light year behind you, that's running according to your telescope observations at half speed. These telescope observations could be made of clock with rotating hands, a digital clock digital numbers, or even red-shifted atomic spectral line.

We'll leave the issue of how you look at the clock so far behind you without opening the window mostly unspecified. Maybe you have instrument readings from a video feed or something.

With the window closed, you might draw one diagram with your "gravitational field lines". There will probably be some disucussion about what that diagram actually means if you show it to someone who is familiar with GR. What do these lines you've draw on this diagram really represent?

When you open the window, you look at the same clock. It's still running at the same half-rate, absolutely nothing has changed with how the clock behaves when you open the window. But now you crumple up your first diagram, and you draw a second diagram that shows the doppler shift of the light emitted from the clock, and how it redshifts by a factor of 2:1 as you accelerate away from the clock, because it takes time for the light emitted from the clock to catch up with you, and during that time you're accelerating away from the clock, causing all your observations to be red-shifted and time delayed.

It might be hard for you to draw this diagram, I don't know. It's a worthwhile diagram, though.

In either of these diagrams, the clock running at half-rate runs at half-rate. But your explanation for "why" the clock is running at that speed changes depending on which diagram you use.

Note that you can build an instrument, sometimes called a Forward Mass detector, <<wiki link>>, that will produce a signal if there is a mass close enough behind you, and won't produce a signal if there is not, that will work without opening the window. The device relies on measuring gravity gradients, also called tidal forces, and will only work if the mass is sufficiently close. If the mass is the Earth and you're standing on it, the detector will easily detect the Earth's presence. But if the mass a very huge mass (say millions or billions of solar mases, from a huge black hole) that is very far away, the detector won't necesarily be sensitive enough to detect the distant mass. But in that case, if you're that far away from the mass, you'll not reasonably be standing on it. You'll be in a space-ship.

Note that you also might be on a spaceship even if you're on the Earth. The spaceship could be wastefully burning fuel in order to hover a short distance (or even a longish distance) above the ground.