# Now when we can measure gravitational field, how does the principle of equivalence hold true?

LIGO measured gravitational field waves.

The whole thought experiment of Einstein, leading to ‘principle of equivalence’, assumes that there is no way to know inside the rocket that whether its accelerating or things are acting under gravitational field.

Now, how does this still hold true?

• What makes you think that the detection of gravitational waves by LIGO may invalidate the principle of equivalence? – Bob D Feb 24 at 21:29
• @BobD You are in a rocket, and now you can measure gravitational field, so you can know for sure whether it's accelerating or if there is gravity - which you can't according to 'principle of equivalence'. – amsquareb Feb 24 at 21:32
• You can measure gravitational waves, but you can not measure whether you feel a weight because you're still in a gravity field or you're accelerating. – md2perpe Feb 24 at 21:39
• Doesn't the equivalent principle hold only locally? – Alfred Centauri Feb 24 at 22:17
• What Alfred said. The LIGO apparatus makes measurements over a region of space, not local measurements. You can easily determine whether a rocket is sitting in a planet's gravitational field or accelerating in free space by measuring the acceleration at the top & bottom of the rocket. In a planet's field the gravity is slightly weaker at the top. – PM 2Ring Feb 24 at 22:49

Now, how does this (the principle of equivalence) still hold true?

First of all, I do not profess to have a deep understanding of general relativity (GR). My answer is based on my admittedly superficial understanding. Therefore, I am sure others can answer better, and I encourage them to do so, as it may help me understand it better.

I believe the equivalence principle would still hold true, because I think it in effect says a local gravitational field having acceleration $$g$$ is indistinguishable from the rocket undergoing an acceleration of $$g$$. I should think that if the LIGO apparatus were placed in the rocket (it would have to be a very, very long rocket!) and detected gravitational waves, those waves would be due disturbances in the fabric of space time due to non local violent accelerations of large masses. This, however, should have little or no effect on the local measurement of g.

I think the rocket measurement of a non varying gravitational field may be somewhat analogous to measuring an electrostatic field (field due to stationary charge). The LIGO measurement of a time varying gravitational field (gravitational waves) due to violent accelerations of large masses may be somewhat analogous to measuring electromagnetic waves due to acceleration of electrical charge. Both the gravitational waves and electromagnetic waves travel at the speed of light. However, the violent accelerations of large masses would be occurring very far away from the detectors (and the rocket), otherwise the detectors and those operating them would not survive.

Hope this helps.

LIGO measured gravitational field waves.

False. To answer your question we need to be more specific: It actually measures the time it takes a beam of light to travel down a long tube, bounce off a special mirror, then come back. And it does this for two perpendicular tubes. The time of flight tells you the length of the tubes, since we know the speed of light very accurately. Therefore LIGO is an accurate tube-length measuring device.

Anything that alters the length of the tubes will be detected, including the contraction and expansion of space time as a gravitational wave passes. But accelerations of the tubes by mundane sources can also alter the tube length (including wind, earthquakes, local traffic, and farm equipment to name a few).

### edited:

Going back to the equivalence principle, place a LIGO inside a rocket in deep space and then accelerate that rocket back-and-forth and side-to-side just like a gravity wave. The LIGO wouldn't be able to tell the difference between this and a real gravity wave, just as the equivalence principle predicts.

• Are you saying that if LIGO apparatus is put in a big rocket, and it'a accelerating, then too the LIGO would detect waves? – amsquareb Feb 25 at 6:15
• Yes, If the rocket accelerated back-and-forth and side-to-side just like a gravity wave does, you wouldn’t be able to tell the difference. – cms Feb 25 at 14:12
• If you can mention this explicitly in your answer, I would accept it, thanks. – amsquareb Feb 25 at 19:58
• @amsquareb edited for clarity. – cms Feb 26 at 18:32