# Equivalency question

1. Nov 29, 2003

### Vosh

I given to understand that you can't tell the difference between accelerating in space and standing in a gravity well, say, the Earth. Isn't it true than in one setting you are adding kinetic energy and is this the difference between the two? Thanks for patience with ignorant questions.

2. Nov 29, 2003

### Ambitwistor

Well, if you're accelerating in space, then you're not adding kinetic energy relative to someone who is also accelerating in space right next to you. Conversely, from the perspective of someone falling past a person standing on the Earth, the standing person's kinetic energy will be increasing.

The point of the equivalence principle is this: if you're shut up in a completely closed room (such as an elevator), so you can't tell if you're on Earth or in space, is there a physical experiment you can do, entirely within the elevator, that can determine whether you're at rest on a planet or accelerating smoothy in outer space?

3. Nov 29, 2003

### wolram

what equipment are you allowed to have in the elevator

4. Nov 29, 2003

### Vosh

If gravity is curved space then how is it a force?

If there were only two objects in space and one moved uniformly towards the other such that its path didn't have to curve at all why would it speed up?

All of this reminds me of the way the outside part of something speeds up compared to the inside part of something when rounding a corner; but I don't know why.

Many thanks for patience with Cromagnon-man.

5. Nov 29, 2003

### Ambitwistor

In general relativity, gravity isn't a force.

If you're talking about how one body gravitaitonally influences the motion of the other, the important point is that a straight trajectory in spacetime is usually a curved trajectory in space.

6. Nov 29, 2003

### Vosh

Huh?

7. Nov 29, 2003

### Ambitwistor

Huh what?

8. Nov 29, 2003

### Nereid

Staff Emeritus
Any equipment you like, as long as you can't 'see' outside the elevator!

So, if the elevator walls are not transparent to EM, of any wavelength; block all cosmic rays; are opaque to neutrinos, ... it wouldn't matter what equipment you had. I guess if you put LIGO into your elevator, ...

9. Nov 30, 2003

### Vosh

I should have said, I don't have any physics training. I don't know what you mean by "space" as oppose to "spacetime".

10. Nov 30, 2003

### hedons

Last edited: Nov 30, 2003
11. Nov 30, 2003

### Ambitwistor

Space is the collection of all possible locations: it is 3-dimensional. Spacetime is the collection of all possible events (locations and times): it is 4-dimensional. If you pick all the spacetime events that occur at the same time (and there are many ways of doing this, because the concept of simultaneity is relative), then you get a 3-dimensional subspace of spacetime, which is space at a given time. (If you pick a different time, you get a different 3-dimensional surface representing space at the different time, because space can change with time.)

12. Nov 30, 2003

### Vosh

That's sort of what I thought you meant. I imagined that diagram of a cube moving through time (animation I saw on pbs once a long time ago) and tracing lines or curves along the way...
Are you saying that my two objects on a straight path for each other actually travel on a curved path as they move through time as well? And I'm not even sure what I just said...

Many thanks.

Last edited: Nov 30, 2003
13. Nov 30, 2003

### Ambitwistor

Yes, although for a freely falling body, it's the other way around: they travel along straight paths in spacetime, but curved paths in space.

14. Dec 1, 2003

### Vosh

I can hear someone asking, "what's the difference between my freely falling bodies heading straight for each other on a straight line (as oppose to one body trying to rush past but getting caught by gravity and curving off its straight course) and one of the bodies being propelled by rocket?"

Isn't everything in free fall until it lands, sometimes violently, on something?

When I picture a space/time diagram, which looks like a cube moving up through time like an elevator, I see an object moving straight through space from, say, left to right, but tracing a diagonal line in space-time... To what degree am I making sense?

I'm wondering, is the model of the 2d net being dipped by a ball so that when you roll another ball on the net it falls into the pit formed by the first ball -- is that just an illustration or did the reasoning for curved space-time actually devolve from that?

I have to go scratch, now. Many thanks!

15. Dec 1, 2003

### Ambitwistor

Freely falling bodies are in free fall: they're weightless.

Everything is in free fall if there are no non-gravitational interactions acting on it.

You've correctly pictured the worldline of an inertial observer in flat spacetime (i.e., in the absence of gravity).

It's just an illustration.

16. Dec 1, 2003

### davilla

acceleration through the Univserse

Being just as confused as Vosh, and looking at Ambitwistor's analogy, I had this simpler question about a glass elevator.

Relativistically speaking, if you're accelerating in a spaceship, there are all sorts of weird things that are supposed to happen, what with light coming in at an angle, mass increasing and red shift as a result of gravitational fields, and changes in the perceived time frames of distant objects. I know could never explain those sorts of things very well, so I hope I've at least labeled them decently.

My question is with regard to the earth, our frame of reference, as a "space ship." Long ago I've seen numbers describing how incredibly fast we move through space--with respect to the Solar System, Milky way, etc. But I'm not sure I've ever seen any numbers describing our rate of acceleration, if any. With eliptical orbits certainly there must be some acceleration. Is there any way to measure this with respect to our galaxy, or whatever cluster/supercluster we're in, or maybe the universe as a whole?

17. Dec 1, 2003

### Vosh

So gravity curves my diagonal line meaning that the object moving from left to right will necessarily move faster on the curved part of the diagonal line; right?

18. Dec 1, 2003

### Ambitwistor

Well... the diagonal line is the object's path through spacetime (worldline). In the presence of gravity, the path is still a "straight line", it's just that the space itself is curved... (Take the surface of the Earth: the equator is a "straight line" on that surface, but the surface itself is curved.)

19. Dec 1, 2003

### Nereid

Staff Emeritus
Here's some data from which OOM (order of magnitude) estimates of the accelerations could be made (in all cases, assume circular motion):
- Earth rotation (at the equator): radius 6,000 km, period 24 hours
- Earth revolution about the Sun: radius 150m km, period 365 days
- solar system revolution about Milky Way centre: radius 25,000 light-years, period 200 million years
- solar system vertical oscillation about the galactic disk plane: 100 light-years, period 25 million years
- Milky Way orbit within Local Group: (later)
- Local Group within Virgo cluster: (later)
- Virgo cluster within {??} supercluster (motion about the Great Attractor): (later)

20. Dec 1, 2003

### Vosh

Do you mean that if I represent just the area of space surrounding my object (instead of all of 3d space) in the cube (elevator) and move it up through time that near another object I should have my elevator's path curve although my object is still moving in a "straight path" from left to right within the cube of space? I hope I'm getting these visuals out coherently. So the space-time line is curved but not the space one, errr, and now I have to look again at your previous post about the difference between free fall and wossname.

I wonder how the idea for "curved space" got started. I mean, what was the beginning of the reasoning that led to it? Did someone see an apple fall in a strong wind? ;)

Oh look! The zookeeper is here with my bananas!

21. Dec 1, 2003

### Ambitwistor

I don't know if I follow.

Ignore one spatial dimension and picture spacetime as a 3-dimensional volume. You can cut it into a stack of 2-dimensional slices, which are space at different times. If you picture the worldline of an object in spacetime, it's a curve in the 3-dimensional volume. Now, project that curve down onto one of the 2D slices: that's the path in space. The projection into one 2D slice can be curved, even if the 3D curve is straight.

Well, people imagined that space could be curved before Einstein (most notably Riemann), but they didn't have a theory of it. Einstein was led to the idea of curved space by considering what would happen to the circumference-to-diameter ratio of a circle as measured from a rotating reference frame, in special relativity. (It's greater than &pi;, which means that space isn't flat.)

22. Dec 1, 2003

### Vosh

Ok, so I have a cube in front of me. There's an object in it. I start time moving. The object begins moving away from me in a straight line, but if I move around to the side and can see that the space-time line is diagonal (as the cube moves up in that space-time diagram thingy). Back in my seat the line looks straight up and down but I know that it's further away from me as it goes up. Projecting it down onto a 2d slice looks straight too... oh, do you mean that the cube *itself* is curved so that if I looked straight down at my diagram from top I would see the curved path, although for those living in that curved space, it's a straight line going through space since they're all curved along with it? That is -- the cube becomes curved near a mass, I mean, naturally...

Many thanks.

Uhh, I better not look at that right now. ;)

23. Dec 1, 2003

### Vosh

Uhh, oh. Hang on a minnit...

24. Dec 2, 2003

### Vosh

I have to try this again.

An object moves from left to right. Start with one 2d slice, a moment of time. Begin adding more slices. A cube forms and the object traces a diagonal line from bottom to top. Should I be seeing a curved line, not a diagonal one?

25. Dec 2, 2003

### Ambitwistor

Your earlier post was on target: for this analogy to work, you have to envision the cube itself as intrinsically curved. (But you cannot really visualize this directly.) If you just have an ordinary Euclidean cube and flat spatial slices, then a straight line through the cube will project down to a straight line in the spatial planes.

On the other hand, if you picked some kind of wrinkly surface to slice the cube into, then even if you have a flat spacetime (cube), you can have curved space, and a straight line in spacetime could project down onto a curve in space.