# Is a change in earth's surface gravity detectable?

1. Aug 1, 2004

### Creator

Since my question relates to gravitational field I've placed it here under Gen. Rel. section to encourage more knowledgeable ideas & responses from those who are gravitationally astute.

Here's my question:
If the earth were to increase its gravitational field at the surface (for whatever reason), would one be able to detect that increase with non-inertial measurements?
I mean, would one be able to detect it with methods other than weight changes, mass or inertial changes (like gravitometers), etc.?

For example. to be more specific, is it possible to detect a brief change in earth's gravity field with a laser interferometer? Let's say an interferometer that is oriented with one arm pointing upward (vertical) for a hundred meters, and the other arm placed horizontal to the earth's surface for 100 meters? A laser source of specific frequency located near the vertex passes light thru a beam splitter, reflects it off the end of each arm and back to the vertex where a detector registers the interferebnce pattern, (as in a usual interferometric setup).

Let us assume for simplicity the field is constant for the vertical distance of the vertical arm (no field gradient) and equal to the field in the horizontal direction. Now the earth's gravity field changes abruptly for, say, a few seconds or so while we are monitoring the interference pattern. Assuming the interferometer is sensitive enough, will the gravity change be detectable? Will there be a shift in the pattern? Why or why not? Does the velocity of light change with a field change? Does the frequency change so as to make the gravity variation detectable?
Can someone interested enough give me some logical supporting opinions please?

Creator

Last edited: Aug 1, 2004
2. Aug 2, 2004

### pmb_phy

I guess you could look for changed in gravitational redshift, i.e. the change in frequency of light as it climbs up the gravitational field.

Pete

3. Aug 5, 2004

### pervect

Staff Emeritus
I think that this measurement would, in practice, wind up being in the class of inertial measurement that you want to avoid. You can think of the laser beam measurement of distance as being a stiff rod - as stiff as anything ever gets (there's no such thing as a rigid body in relativity). So what you'd be measuring with your interferometer is the difference in stiffness between your laser beam, and your physical construct, i.e. you'd be measuring the displacement due to the change in force on a spring, the spring being the physical arm of your interferometer, which would be less rigid than your laser beam.

4. Aug 5, 2004

Im not that knowledgable with inferometers, but if you were to increase the earths gravity, no matter where you were, that would in turn bend space time a little more and would make oblects traveling in the curved spacetime seem like they are traveling a longer distance. If I remember correctly, the accounted distance is $$D = m/3c^2$$ where $$m = mass \ D = extra \ distance \ and \ c = speed of light$$ This extra gravity added to the earth would elongate the distance traveled by the laser beam and would in turn give you a different interference pattern.

Last edited: Aug 5, 2004
5. Aug 5, 2004

### Nereid

Staff Emeritus
To answer Creator's general question, yes, and pmb_phy got the obvious method - gravitational redshift. Gravitational time dilation would be another obvious method.

In principle, all ( ) you'd need to do would be to repeat the classic 1960's Pound, Rebka and Snyder redshift experiment, and the 1976 Scout rocket time dilation one. Some background here.

Of course, you'd have to find a way to increase the sensitivity by ~>3 OOM

6. Aug 5, 2004

### pervect

Staff Emeritus
I don't see this. If you changed the potential energy of the whole setup, you could change the metric coefficeints, I suppose, i.e. the length of the meter would be different.

But let's consider a thought experiment. Let's measure the length of a 1 meter bar with a laser. Now let's fly the bar into outer space, where g_00, g_11, etc are different, and measure the length again with a laser. We will measure the exact same length we measured on the ground, because the metric change will affect the bar and the interferometer equally.

7. Aug 6, 2004

### Imparcticle

Apparently, it is impossible to detect a change in earth's gravitational strength without inertial measurements, right? All of the methods presented at least involve an intertial measurement...right?

8. Aug 6, 2004

### Nereid

Staff Emeritus
Would you please explain how a measurement of the gravitational redshift involves an inertial measurement?

9. Aug 6, 2004

### Garth

A good question, the next question is, "What would change (fundamental particle masses, lengths of rulers, clock rates) with the gravitational field?" The answer to which is theory dependent. If that theory is GR then you don't expect the gravitational field to change in the first place, unless the Earth's mass or radius changes, due to a massive impact for example.

10. Aug 6, 2004

### pervect

Staff Emeritus
Takin the empirical approach, I did a quick google search for accelerometers. There were several references for laser gyro's, but none for laser linear accelerometers. The wikipedia link was representative