Last week, my newsletter focused on the muon paradox; now let’s look at the transit of Mercury. General relativity predicts that, due to the curvature of spacetime around the sun, the perihelion precession of Mercury should advance slightly more than is indicated by Newtonian gravity.
General relativity predicts that the shift of its orbit during perihelion will change by an additional 43 arcseconds per century. This is close to the observed discrepancy, and it gave Einstein confidence to advance his theory. However, the amount of the required deviation was already known, so Einstein fudged his math to account for the shift.
Clocks on Earth can not accurately measure the speed or duration of objects experiencing a different environment. In part 1, we saw that muons reach the surface of Earth, not because of time dilation, but because our clocks have built-in gravitational time dilation.
The primary difference between Newton and Einstein lies in the fact that a clock is affected by strong gravity, necessitating the need to account for the clock's time dilation. Thus, one second of accelerated motion of Mercury near the sun happens in less time than what we view from Earth. That means the orbital speed is faster near the Sun because speed is defined as distance per time; therefore, if the time is shorter, the speed is faster, and it will create a greater shift in Mercury's orbit around the Sun. Consequently, this is not due to Einstein's relativity.
The forces of nature can explain everything without the relativity of time if you prefer the idea that space curves and time shifts. Be my guest and stick with the 115-year-old theory. However, we should employ critical thinking and rethink relying on mathematical ideas.
Einstein's Precession of Mercury
Einstein demonstrated that general relativity closely agrees with the observed amount of perihelion shift. This was a decisive factor motivating the adoption of general relativity. (source: Tests of general relativity, Wikipedia, the free encyclopedia).
Einstein proposed that the perihelion precession of Mercury be measured using the field equations presented in his 1915 paper to test his general theory of relativity. It was done several times regarding Mercury’s orbits, showing that his equations were accurate.
The following seven points arise:
1. Relativity is not required to explain the perihelion precession of Mercury. It's easily explained by the gravitational effects of the Sun and nearby planets. Furthermore, all orbiting planets in the Universe undergo a perihelion precession; it's just that Mercury’s perihelion precession (i.e., shifting elliptical orbit) is very pronounced.
2. Today’s astronomers can accurately measure Mercury's perihelion precession using modern astronomical technology that does not involve any kind of Einsteinian relativity. Furthermore, General Relativity only gives approximations of perihelion precessions. The 1915 paper mentioned was a set of manipulated equations specifically designed to yield an exact result for the perihelion precession of Mercury and Mercury only.
The math doesn't solve it entirely, and it only gives approximations for calculating orbital arcs (an arc is the amount of shift from one elliptical orbit to another).
3. Normally, the amount of orbital arc from one orbit to another is nearly the same. But in Mercury's case, each orbital arc (each shift into a new orbit) is very pronounced. This discrepancy was calculated to be 43 seconds of arc per century, a value well-known before Einstein's time.
Why so? Because Newton's equations, taking into account all the effects from the other planets (as well as a very slight deformation of the sun due to its rotation) and the fact that the Earth is not an inertial frame of reference, predict a precession (change) of 5557 seconds of arc per century. This amounts to a discrepancy of 43 seconds of arc per century. But Newton’s equations could not explain mathematically the cause of the 43” arc anomaly.
4. Einstein knew about Newton’s 43” arc anomaly and indeed based his arc calculations on Newton’s work. Einstein wanted to present a method for calculating Mercury’s 43” arc anomaly (but based on his relativity field equations) to prove the veracity of his general theory of relativity. However, given the nature of relativity, Einstein's field equations could only give an approximation for the perihelion precession of Mercury (not an exact calculation showing how the 43” arc anomaly arises).
5. To resolve Einstein's conundrum, he collaborated with Karl Schwarzschild, a German physicist and astronomer of the time. Schwarzschild reviewed Einstein’s equations, and he came up with a solution to make Einstein's field equations produce an exact result for the 43” arc anomaly rather than just an approximation. Schwarzschild did this by employing a mathematical ‘trick’ to make Einstein's Field Equations provide a close (exact) solution relating to the perihelion precession of Mercury.
“Schwarzschild found a simple trick that allowed him to avoid the problem of the non-allowed coordinates [of spacetime]. He created new variables for the spherical coordinates of the determinant 1 to the power of 21. Einstein's field equations and the coordinate condition of the square root of minus g from his November 18 paper were satisfied. So, returning to the non-allowed spherical coordinates, we arrive at the exact solution to Einstein's problem and to the mathematical singularity in the solution when R = 0." Source: Galina Weinstein, ‘Einstein-Schwarzschild-the Perihelion Motion of Mercury and the Rotating Disk Story,' Tel Aviv University, 2014.
Note: The ‘Schwarzschild Metric,’ as it is known today, can accurately measure the amount of shift in planetary elliptical orbits. But the Schwarzschild Metric is a set of equations based on (but not the same as) Einstein's General Relativity field equations. Thus, the Schwarzschild Metric shows that the relativity field equations can only give rough approximations for measuring the movements of astronomical objects unless the field equations are adapted (changed) to the Schwarzschild Metric.
6. In short, Einstein manipulated his relativistic equations (with help from Schwarzschild) to make such equations give an exact result for a particular instance, i.e., an exact result that corresponded with Mercury’s orbital anomaly. Furthermore, in manipulating the equations, Einstein employed covariance algebra, a type of mathematics that is largely discredited today. It is discredited mainly because covariance is not a reliable measure of the strength of a linear relationship. After all, it's not invariant to deterministic linear transformations. As such, covariance allows a wide range of results from which you can choose the result that most suits you.
7. In 1915, Einstein published his general theory of relativity, which is well known. But it can only give approximations for calculating Mercury’s 43” arc anomaly. Back in 1915, Einstein wanted to show that his general theory involving spacetime curvature could accurately calculate the 43” arc anomaly. To clarify, he was not predicting the occurrence of the 43” arc anomaly (a popular misconception) as the anomaly was already well-known; instead, he was showing that relativity can be used to calculate the 43” anomaly precisely.
So, as his 1915 paper on General Theory could only give approximations for the 43” anomaly, he needed a mathematically exact solution specific to mercury. As mentioned, he collaborated with Schwarzschild, and in 1916, Einstein presented a version of his general relativity, but with the mathematics manipulated specifically for the perihelion precession of Mercury. At the time, this proved to be a decisive factor in motivating the adoption of general relativity, particularly in the absence of a more credible theory of gravity.
Thus, when Einstein proposed that his general theory of relativity could be used to predict precisely the amount of the perihelion precession seen in Mercury, he already knew beforehand that he would get the precise result he was predicting, having rehearsed his contrived calculations. In modern speech, it was a ‘setup’. Is it time to rethink Einstein's mental experiments, which cause time and space to change?
Thank you for following my weekly newsletter at "Science in Your Life." In my current articles, I am exploring time and Einstein's Relativity to find if we can interpret relativity using clocks instead of the speed of light. See you next time. Take care. xo