What do we actually see

 1 Introduction 

The main purpose of this article is to delve into how nonlinear is the process of scientific discovery and also to emphasize the fact that we are in fact sitting on shoulders of giants rightly said by Sir Issac Newton Before anything else, I’ll start with a fact(which you probably have heard or thought about before) that is so simple but surprising which is whenever we look at something(anything), we look at the past sort of like a time machine because photons, which is how we humans typically observe as they carry the information of what we are trying to look at, reflecting from any object take time to reach our eyes, now it isn’t much when we are observing nearby objects as time it takes is low. Still, when it comes to far-away objects in space, it gives us a way to look so long back that we can get information relating to how we all came into existence, which is profound in some sense. Now when it comes to observation from earth there are some issues we face. I am sure you all have heard, at least for me it was told, about how the universe we observe is isotropic that is in any direction we look we don’t see any difference at large scale and evidence for it was cosmic microwave background observation who accidental discovery(read about it) is a fascinating example of science progress, without digressing much, be any point on CMB map has a thermal black body spectrum at a temperature of 2.72548±0.00057 K. This low difference of temperature contributes to isotropic nature. As shown in the figure below it might look like there is a large difference in color but that corresponds to 0.00057K.

Figure 1: The Cosmic microwave background(CMB) as observed by Planck

Understanding this observation, it seems fair conclusion, but you have to remember the important point that CMB was first recorded from observation of electromagnetic radiation from the earth, now we know the basic fact that the earth is moving(at a high speed), if the universe is isotropic we should see a directional bias towards the direction we are moving in which follows a particular equation derived in special relativity. This gives us a dipole type of observation as shown in the Figure 2 below

Figure 2: The Cosmic microwave background(CMB) as dipole

Now for those of you who haven’t come across an observation of radiation from a moving source, Here’s an analogy, Assume Case 1 that it’s raining about your head completely perpendicularly and you can watch every droplet falling in a straight line perpendicular to the ground, but rather than being in rest, Case 2. is you are driving a car(or running) in same uniform rain, try to watch rain droplets(imagine), they will be falling tilted towards you when you watch them, hence a directional bias. 

It took some time for people to verify this and now standard known that CMB follows that equation and forms a dipole-like shape, which is as it should have been if special relativity is correct because the analogy I gave you is classical as you driving the car is not at very high speed, so the equation of special relativity is more accurate than our analogy. This is one of many cases that shows you that we have to be careful to interpret what we observe and what is present. Now I will talk about another accidental discovery which is called aberration of light which was done by James Bradley along with Samuel Molyneux while attempting to discover stellar parallax. 

Parallax is easy to understand as we observe it daily, Parallax is just a fancy name for it. We can do a simple exercise(or you can google it I have attach a simple reference[5]), extend your arms horizontally up and hold your thumb up, now focus on your thumb through just the right eye and notice the background, and then close the right eye and observe through the left eye, and observe the shift in the background due to the shift in observation eye, now imagine if you clicked a picture keeping the background same in both frames, you would notice shift in position of thumb in both pictures, but this is just an apparent change, due to change in observation point. when this same thing happens, due to a change in the position of Earth in the solar system we change our observation point in space and then we call it Stellar parallax. 

Coming back to our story of accidental discovery, Bradley and Molyneux decided to observe the star Gamma Draconis for stellar parallax, which comes directly overhead, near the Pole star, thereby minimizing the displacement of rays by refraction in the Earth’s atmosphere. Figure 3 shows their high precision 24-foot telescope, made by George Graham (1675-1751), which was fixed to the internal side of the chimney in Molyneux’s house, extending to a hole in the roof. The angular resolution was about 1”. It was found that body heat was enough to disturb the plumb line, and the motion of the plumb bob was damped by immersion in water. Air currents were reduced by enclosing the plumb line in a tube, but this provided a home for spiders and their webs which had to be removed from time to time. To make the observations, starting on December 17, 1725, James or Molyneux would lie on the couch by the fireplace looking up into the telescope’s eyepiece. A calibrated micrometer was used to swing the telescope between the star and the plumb line and measure the star’s north-south deviation when it crossed an east-west cross-hair. This was repeated for two years. Unfortunately, In this effort, they failed because the angle was too small to be seen by the instruments of that

Figure 3: The chimney in Molyneux’s house in Kew Gardens in 1725, showing Bradley’s telescope attached

time period, and stellar parallax (of 0.3”) would not be detected until the work of Bessel in 1838.

Bradley’s discovery of the aberration of light, while investigating stellar parallax, illustrates the non-linear path of scientific discovery—how a quest for one answer can lead to an entirely different, groundbreaking realization. This mirrors how observation of the Cosmic Microwave Background, initially thought to be noise, became one of the most significant observations in cosmology. Hence what they saw didn’t match the expected result that they set out to achieve, but shifted by precisely 90 degrees. They observed a shift that wasn’t due to parallax and every time shifted by a phase of 90 degrees which no one could understand why. In the end, James Bradley gave the final explanation citing the fact that we need to take into account the motion of the earth, mathematical analysis is done below, The Amazing part is it also disproves the case of stationary ether(think how), and the explanation is almost similar to the one about the car that I first presented but in this case, the Car is earth and instead of umbrella you have a telescope, just like an umbrella you have to tilt the telescope to observe to star and that angle you have to shift will change because the direction of earth’s velocity changes during it’s a revolution around the sun. Why is direction of the earth’s velocity important can be understood by the analysis that follows, which will conclude that a change in the direction of the earth’s velocity will change the direction of relative velocity which in turn will change direction of tilt.

Classically this can be shown in Figure4, we can calculate the angle of tilt required by using speed of the earth in the solar system V _E and the speed of light V _L, where V _LE = V _L − V _E is relative velocity and tan(θ) = |V _E | |V _L | . This mathematical interpretation of Bradley’s data fitted well with all his observations. His best estimate of the average value of θ was 20.25” compared with today’s value of 20.47” was a remarkable achievement. Now for some of you, this might seem simple and it is now simply explained, but you have to imagine how long ago this discovery was made, in the 1700s when people were still debating whether Earth followed the Copernican model or not, when you need to be rich or convince someone rich to conduct observation when we didn’t have satellites to give you high precision results, which seem trivial now but weren’t remotely obvious to people then. I’ll end with a quote from Galileo Galilei:

 “All truths are easy to understand once they are discovered; the point is to discover them.” 

2 Bibliography

1. Lightspeed: The Ghostly Aether and the Race to Measure the Speed of Light (https://academic.oup.com/book/ 32357/chapter-abstract/268621906?redirectedFrom=fulltext)

2. Bradley’s 8-foot Transit Instrument (1750) (http://www.royalobservatorygreenwich.org/articles.php?article=1296)

3. Bradley’s letter about what he discovered, 25 pages long IV. A letter from the Reverend Mr. James Bradley Savilian Professor of Astronomy at Oxford, and F. R. S. to Dr. Edmond Halley Astronom. Reg. giving an account of a new discovered motion of the fix’d stars. (https://royalsocietypublishing.org/doi/epdf/10.1098/rstl.1727.0064)

4. https://en.wikipedia.org/wiki/Aberration 5. Excercise of parallax: https://www.coe.edu/faculty-staff/james-wetzel/astronomy/parallax

-- Arpit (MS22)