# Gravity Probe A

Gravity Probe A (GP-A) was a space-based experiment to test the equivalence principle, a feature of Einstein's theory of relativity. It was performed jointly by the Smithsonian Astrophysical Observatory and the National Aeronautics and Space Administration. The experiment sent a hydrogen maser, a highly accurate frequency standard, into space to measure with high precision the rate at which time passes in a weaker gravitational field. Masses cause distortions in spacetime, which leads to the effects of length contraction and time dilation, both predicted results of Albert Einstein's theory of general relativity. Because of the bending of spacetime, an observer on Earth (in a lower gravitational potential) should measure a different rate at which time passes than an observer that is sufficiently high up in Earth's atmosphere (at higher gravitational potential). This effect is known as gravitational time dilation.

The experiment was a test of a major fallout of Einstein's general relativity, the equivalence principle. The equivalence principle states that a reference frame in a uniform gravitational field is indistinguishable from a reference frame that is under uniform acceleration. Further, the equivalence principle predicts that phenomenon of different time flow rates, present in a uniformly accelerating reference frame, will also be present in a stationary reference frame that is in a uniform gravitational field.

The probe was launched on June 18, 1976 from the NASA-Wallops Flight Center in Wallops Island, Virginia. The probe was carried via a Scout rocket, and attained a height of 10,000 km (6,200 mi), while remaining in space for 1 hour and 55 minutes, as intended. It returned to Earth by splashing down into the Atlantic Ocean.

## Background

The objective of the Gravity Probe A experiment was to test the validity of the equivalence principle. The equivalence principle was a key component of Albert Einstein's theory of general relativity, and states that the laws of physics are the same regardless of whether you consider a uniformly accelerating reference frame or a reference frame that is acted upon by uniform gravitational field.

### Equivalence principle

The equivalence principle can be understood by picturing a rocket ship in two scenarios. First, imagine a rocket ship that is at rest on the Earth's surface; objects in the rocket ship are being accelerated downward at 9.81 m/s². Now, imagine a rocket ship that has escaped Earth's gravitational field and is accelerating upwards at a constant 9.81 m/s² due to thrust from its rockets; objects in the rocket ship that are dropped will fall to the floor with an acceleration of 9.81 m/s². This example shows that a uniformly accelerating reference frame is indistinguishable from a gravitational reference frame.

Further, the equivalence principle guarantees that phenomena that are caused by inertial effects will also be present due to gravitational effects. Imagine, for example, a beam of light that is shined horizontally across a rocket ship that is accelerating uniformly upwards. According to an observer outside the rocket ship, the floor of the rocket ship accelerates up towards the light beam. The light beam does not seem to travel on a horizontal path according to the outside observer, rather the light seems to bend down toward the floor (because the floor is accelerating uniformly upward). This is an example of an inertial effect that causes light to bend. The equivalence principle states that this inertial phenomenon will also occur in a gravitational reference frame as well. Indeed, the phenomenon of gravitational lensing states that matter can bend light, and this phenomenon has been observed by the Hubble Telescope.

### Time dilation

Time dilation refers to the expansion or contraction in the rate at which time passes, and was the subject of the Gravity Probe A experiment. Under Einstein's theory of general relativity, matter distorts the surrounding spacetime, so that space gets bent similarly to the way a sheet of fabric would bend if a bowling ball were dropped in the middle of the sheet. But the distortion manifests itself in the time direction as well: time would appear for a distant observer to flow more slowly in the vicinity of a massive object. For example, the metric, surrounding a spherically symmetric gravitating body, has a smaller coefficient at $dt^{2}$  closer to the body, which means slower rate of time flow there.

There is a similar idea of time dilation occurrence in Einstein's theory of special relativity (which deals with neither gravity nor the idea of curved spacetime). Such time dilation appears in the Rindler coordinates, attached to a uniformly accelerating particle in a flat spacetime. Such a particle would observe time passing faster on the side it is accelerating towards and more slowly on the opposite side. From this apparent variance in time, Einstein inferred that change in velocity affects the relativity of simultaneity for the particle. Einstein's equivalence principle generalizes this analogy, stating that an accelerating reference frame is locally indistinguishable from an inertial reference frame with a gravity force acting upon it. In this way, the Gravity Probe A was a test of the equivalence principle, matching the observations in the inertial reference frame (of special relativity) of the Earth's surface affected by gravity, with the predictions of special relativity for the same frame treated as being accelerating upwards with respect to free fall reference, which can thought of being inertial and gravity-less.

## Experimental setup

The 100 kg Gravity Probe A spacecraft housed the atomic hydrogen maser system that ran throughout the mission. Maser is an acronym for microwave amplification by stimulated emission of radiation, and is similar to a laser, as it produces coherent electromagnetic waves in the microwave region of the electromagnetic spectrum (as opposed to lasers which produce light in the visible or ultraviolet region). The probe was launched nearly vertically upward to cause a large change in the gravitational potential seen by the maser, reaching a height of 10,000 km (6,200 mi). At this height, relativity predicted a clock should run 4.5 parts in 1010 faster than one on the Earth.

### Doppler shift

Along with the hydrogen maser, a microwave repeater was also included in the probe in order to measure the Doppler shift of the maser signal. A Doppler shift occurs when a source is moving relative to the observer of that source, and results in a shift in the frequency that corresponds to the direction and magnitude of the source's motion. The maser's signal is Doppler shifted because it is launched vertically at a high speed relative to the Earth, and the results from the maser need to be Doppler shifted in order to be correctly understood.

According to the 1976 press release by Joyce B. Milliner: "The interaction of the electron and proton in the hydrogen atom generates a microwave signal (1.42 billion cycles per second) stable to one part in a quadrillion (1 x 10−15), or the equivalent of a clock that loses less than two seconds every 100 million years."

## Results

The goal of the experiment was to measure the rate at which time passes in a higher gravitational potential, so to test this the maser in the probe was compared to a similar maser that remained on Earth. Before the two clock rates could be compared, the Doppler shift was subtracted out of the clock rate measured by the maser that was sent into space, to correct for the relative motion between the observers on Earth and the motion of the probe. The two clock rates were then compared and further compared against the theoretical predictions of how the two clock rates would differ. The stability of the maser permitted measurement of changes in the rate of the maser of 1 part in 1014 for a 100-second measurement.

The experiment was thus able to test the equivalence principle. Gravity Probe A confirmed the prediction that deeper in the gravity well the time flows slower, and the observed effects matched the predicted effects to an accuracy of about 70 parts per million.