# Thread: How real is general relativity?

1. By the way, if you're interested in reading more about the example Ken G brought up, it's a pretty classic question, usually called "Bell's spaceship paradox". You can read more detailed treatments with some nice graphs here or here or Wikipedia, of course. As with many tricky relativity questions, sometimes seeing it explained in different ways can help you "get it".

2. Been thinking about the replies above for a while.

Should my question be: Are size effects in GR as real as length effects is SR?

Consider an accelerating lift or rocket.
Think of 'up' the direction of acceleration.

Acceleration is the same as gravity, so clocks at floor level are running slower than clocks at ceiling level in the rocket.
This corresponds the the back/floor of the rocket being redshifted relative to the front/top. You could rig the rocket with laser to show the corresponding gravitational red/blue shifts in and against the direction of acceleration.
The lasers demonstrate observers above and below the rocket see the bottom of the rocket redshifted relative to the top. It looks to be true for all observers.

You could then imagine the roof of the rocket and floor of the rocket rigged with lasers in all directions.
To me it looks valid to use the classic special relativity train thought experiments in reverse to calculate a relative path length from a time dilation. (Ok?)

This gives you the result that the floor of the rocket is larger than the ceiling. So you can then describe the properties of the matter in the floor relative to the ceiling.

This looks identical to the clock on a neutron star version but with no gravity curving space.

3. Originally Posted by PetTastic
Been thinking about the replies above for a while.

Should my question be: Are size effects in GR as real as length effects is SR?

Consider an accelerating lift or rocket.
Think of 'up' the direction of acceleration.

Acceleration is the same as gravity, so clocks at floor level are running slower than clocks at ceiling level in the rocket.
This corresponds the the back/floor of the rocket being redshifted relative to the front/top. You could rig the rocket with laser to show the corresponding gravitational red/blue shifts in and against the direction of acceleration.
The lasers demonstrate observers above and below the rocket see the bottom of the rocket redshifted relative to the top. It looks to be true for all observers.

You could then imagine the roof of the rocket and floor of the rocket rigged with lasers in all directions.
To me it looks valid to use the classic special relativity train thought experiments in reverse to calculate a relative path length from a time dilation. (Ok?)

This gives you the result that the floor of the rocket is larger than the ceiling. So you can then describe the properties of the matter in the floor relative to the ceiling.

This looks identical to the clock on a neutron star version but with no gravity curving space.
My bold. Are you sure about that? Check out the link below.

https://www.einstein-online.info/en/...nce_principle/

If I understand correctly, the rocket-propelled laboratory in deep space and the one on the ground only experience the equivalence throughout if they are infinitesimally small compared to the gravitational gradient on and near the Earth. Aboard the rocket I expect the clocks to run at the same rate and dropped balls to "fall" in parallel paths, as observed from within the lab. If the rocket is shut down and is near the Earth, only one point in it will be in true free fall. All other parts of it are forced out of free fall, with the tendency to spaghettify if the gradient is strong enough or the rocket's structure is weak enough.

Once again, don't take this as gospel. I am here to learn as well as comment. If anyone thinks I am misinterpreting the article, or thinks the article is seriously flawed, fire away.

4. There is actually a time dilation gradient in the accelerating rocket, too, though it is different from that in the vicinity of a massive object.
In terms of general relativity, the difference is between the Schwarzschild metric (gravitating mass) and the Rindler metric (accelerating rocket).
You can't use special relativity easily in either case, though you can reproduce the observations within the Rindler metric by integrating your way through all the instantaneous rest frames occupied by (say) the front and back of the rocket.

Grant Hutchison

5. Originally Posted by grant hutchison
There is actually a time dilation gradient in the accelerating rocket, too, though it is different from that in the vicinity of a massive object.
In terms of general relativity, the difference is between the Schwarzschild metric (gravitating mass) and the Rindler metric (accelerating rocket).
You can't use special relativity easily in either case, though you can reproduce the observations within the Rindler metric by integrating your way through all the instantaneous rest frames occupied by (say) the front and back of the rocket.

Grant Hutchison
Oops, it appears that I still have a lot to learn. Is the difference, in principle, recognizable by the observer aboard the rocket?

6. Originally Posted by Hornblower
Oops, it appears that I still have a lot to learn. Is the difference, in principle, recognizable by the observer aboard the rocket?
Yes. By suitable experiments, you should be able to determine which metric applies. The most obvious example would be that there are no compressive tidal forces at right angles to the acceleration axis in Rindler, but there are in Schwarzschild. So, as you say, the equivalence principle applies only within volumes so small that tidal gradients are too small for the observer's experimental apparatus to detect.

Grant Hutchison

7. Thought experiments with lasers are fun in this context.
Place 4 lasers on the rocket.
Two pointing up on the floor and top, two pointing down on the ceiling and underside.
The laser on the floor hits the ceiling gravitationally redshifted, the one on the ceiling hits the floor gravitationally blueshifted.
Then cut holes in the floor and ceiling so you can compare the colour of the beams from inside with the light from the lasers on the underside and top.
The taller the rocket the larger the effect.

As far as I can see, the observer in the rocket sees these effects as equivalent to gravity as long as the rocket is small compared the the object causing the gravity.
Shine a laser across the spaceship and the dot on the wall is lower on the wall the other side in a constant manner but only if all external observers see the bottom of the rocket as wider/larger than the top.
Otherwise a laser going across near the ceiling behaves differently from a laser near floor level.

This makes the size effects in general relativity directly equivalent to the length effects in special relativity.
So the size of matter is not fixed GR can change it.

I had better stop here as to me this breaks the fundamental assumption of big bang cosmology.

8. I checked that there was a thread about relativity and jerk, before I joined, and it covers my thinking on reading this thread again. We have covered accelerating rockets but rate of acceleration, jerk, moves toward bullets and then any massive particle setting off, for example an electron being emitted from an atom. Jerk seems to be hard to consider in GR, where constant acceleration is the start point. In an earlier post I mentioned the recent finding of gradual quantum events, rather than instantabeous collapse of wave function. So in the years since the relativity jerk thread, has it become clearer what to understand about extreme jerk? Or should this be a new thread revisiting relativity and jerk?

9. I am not questioning any elements of general relativity. The deeper you embrace it the more beautiful it gets.

The idea of Jerk and applying forces or doing work in an accelerating reference frame is highly interesting.

Think about applying a force to do work and move an object a distance in the direction of acceleration.
Say, the object is moved from the floor to the ceiling of the rocket.
When movement has stopped the object is heavier, smaller, faster and blue-shifted.
Gravitational potential energy is just like storing energy in the binding forces of a spring or battery.

But this only works if GR can change the size of matter.

When using a heavy ball on a stretchy membrane to explain gravity to kids or people like me, you should draw the picture of the planet or star on the membrane first.
So then the heavy ball is placed on top the picture of the planet or star is deformed by the curvature of space-time.

Big Bang cosmology needs to come with the caveat "Assuming the size of matter is the one unchanging thing in the universe."

If you let GR do its thing then all kinds of fun cosmologies are possible. (No claims here about this applying to our universe.)