This is an idea that everyone is intuitively familiar with and will help us put what Einstein changed into context.

We can describe Galileo’s principle of relativity in terms of our 1D figures. Let’s say we have an observer at rest, someone who is standing still, who throws a ball with a constant velocity v. This is described by:

The idea of Galileo’s principle of relativity is that the laws of physics look the same to this person as to someone who is moving at a constant speed with respect to them. From the point of view of someone moving at a constant velocity v (the same as the ball), the ball appears to stand still:

Galileo’s point was that each of these ways of looking at the world is equally valid and is described by the same laws. This observation is a nice trick that can be used when solving problems. Often the algebra needed to describe a problem is simpler in one point of view than another. Building the intuition about what is the simplest POV to take when thinking about a problem is one of the first skills that we teach physics students.

At some deep level you intuitively know this. Let’s say you are traveling somewhere on an airplane. You are at cruising altitude, it’s a smooth ride and the drink service is underway. You have an enormous ~500 mph constant velocity with respect to someone on the ground. However your behavior -- you pouring your $10 beverage into the plastic cup -- is the same as if you were on the ground. You don’t need to account for how fast you are moving. To someone on the ground, you are moving at the same high speed as your drink. From your point of view it is as if you and your overpriced beverage are at rest. This is Galileo’s principle of relativity in action.

Another example. If we have an observer that is moving with velocity v, let’s say in a plane, and he shoots a missile which moves away from the plane at velocity v, then an observer at rest sees the missile moving at a higher velocity, 2v. The total speed of the missile is the speed of the plane plus the speed of the missile relative to the plane. The observer at rest sees the combined speed of the object that is moving and the projectile. In pictures:

You notice this in your everyday life. You are driving on the highway and are overtaking another car. You have the sense that you are slowly moving past them. It takes a while to get around them and move past them. But someone standing on the side of the road would see you both whizzing by.

Galileo’s principle of relativity (which is contained in Newton’s laws) tells us how relative motions combine. To the observer on the ground, the velocities simply add. An obvious consequence is that if the plane is moving faster, the final velocity of the missile is even faster:

In principle, there is no limit to how fast you can make things move. Things can go arbitrarily fast as long as the initial plane (or at some point maybe we need a rocket) was going fast. The missile that gets shot out goes even faster.

Another way of achieving arbitrarily high speeds is by chaining many steps together. One plane, moving at speed v, shoots a missile with speed v. The missile — now moving at 2v with respect to the ground — shoots another smaller missile at speed v, which in turn shoots another... The speed of the final missile shot from this cascade is N×v, where N is the number of steps. Again, with an arbitrarily large number of steps, you can make the final missile travel arbitrarily fast.

Arbitrarily fast things have interesting implications for physics. Regions of space arbitrarily far away can affect what is happening right here and now. In our local neighborhood, if I want to know what is going to happen in the next instant, I now need to track of everything happening in all of space. Regions arbitrarily far away can impact what is going to happen here if there are objects that are moving toward us arbitrarily fast.

Again, this is the situation before Einstein came around. One of the high-level ways you can think about what was revolutionary in Einstein’s Principle of Relativity, is that he limited the range over which things have an effect. He removed this possibility of regions arbitrarily far away impacting what is happening locally now.

We will talk about what it takes to do this next time.

I will use simple diagrams to describe things happening in the world. These diagrams will have space going on the x-axis and time moving along the y-axis; they can describe motion in 1D. For example, a particle or some other object that wasn’t moving in time would be described by a straight vertical line. Whereas something that is moving would be tilted; it changes its spatial position as time moves forward. If the line is straight, we say that the particle has a constant speed or velocity v. Another useful concept associated with this notion of velocity is momentum. If the particle that is moving has a certain mass m, then its momentum is given by p=mv.

One of the things that Newton taught us is that things can also move in curved lines. You can change your velocity, and when there is a change there is an associated force responsible for the change. His work in the Principia laid these foundations.

Not only did Newton tell us how the lines change, he also gave examples of the forces. For example, the force of gravity. If you have two objects with mass separated by a distance r, there is a force between them that you can calculate, given in the equation below.

Since then we have learned that there are other forces, which we now know how to calculate. One example is the electromagnetic force. If two objects have electric charge, there is another force associated with them that is given by a force law that looks similar to Newton’s Gravitational interaction:

So Newton not only taught us how particles move in response to forces, he also taught us how to calculate what the forces are. Again, this is all before the revolution.

A few general comments about this picture of the world. Everything that will happen in the future (or did happen in the past) is encoded in the present. If you know where all the particles are, you can calculate all the forces. If you know how the particles are moving and all the forces you can then to predict where they will be and how they will be moving at the next instant. The world described by this physics is deterministic. The current state of the world plus the laws of physics fixes the next state of the world.

Scientists, and even Newton himself, were not happy about the form of the forces in Newton’s physics. The forces we looked at above are defined and have non-zero values, regardless of how far apart the particles are. If you move one of them, the force on the other one instantly changes without some kind of intermediate messenger. There is action at a distance. All particles somehow know where all the other particles are, even if they are arbitrarily far away.

A final point, with similar implications, is that in Newton’s physics there is no limit to how fast particles can move. This means that particles that are arbitrarily far away, if they are moving sufficiently fast, can affect what happens here in the next instant. So what happens next, in an arbitrarily small time step, depends on the motion and position of all the particles, even those arbitrarily far away. There is an inherent “non-locality” to events in space and time. What happens next, right here, depends on everything happening right now, not just what is happening in our local neighborhood.

This was the conception of what physics was before the revolutions. We will pick up next time on the first revolution: the principle of relativity.

Science at the turn of the 20th century:

Tremendous progress had been made and we had seen some overall convergence of ideas and explanations, but it wasn’t converging fully. It was hitting a wall. It was bottoming out in roughly three subgroups of ideas and explanations: Chemistry, Physics, and Biology. These ideas explained a lot above them, but were more or less self-contained independent disciplines.

Physics was able to explain a lot about the motion of bodies on Earth and in the heavens, but there were certain things it couldn’t explain which were critical to Chemistry, e.g.: atomic spectra. If you look at the light coming from different chemical elements there is a characteristic pattern in the colors, a fingerprint for the element. This was incredibly useful to chemists, who were able to measure these spectra and identify which chemicals were present, in what proportion, and were even able to discover new elements in this way. So this was practically useful and was being applied in chemists’ daily work, but to the physicist, it wasn’t clear at all why these spectra were the way they were; there was no understanding why they should be there and, in fact, physics actually predicted that they shouldn’t be there at all. It was a similar story with biology, which was largely disconnected from physics and chemistry in terms of the techniques and level of explanation used.

Another strange thing this apparent bottoming-out of Newtons dream helps explain is crazy statements from famous scientists about the future of physics.

It seems probable that most of the grand underlying principles have been firmly established and that further advances are to be sought chiefly in the rigorous application of these principles to all the phenomena which come under our notice.

-Albert Michelson

Michelson is basically saying there is nothing new to be discovered in physics. This quote is often trotted out now to show how naive the experts were at the time. But his quote makes perfect sense given his context. In his mind, physics wasn’t about explaining everything; it was obvious that physicists couldn’t explain everything, they couldn’t explain why atoms exist, let alone the strange spectra that came from them. Michelson could know this and still believe physics was more or less finished because he didn’t have our modern conception of Newton’s dream. What he meant by there being nothing new to be discovered in physics is that “physics” was really only the small cluster of explanations shown at the bottom of the figure. Michelson took this to be the way reality was; physics was a distinct discipline and there was no further connection to be made. Adopting this narrow view of physics, he was largely correct.

This picture, however, was radically changed by two 20th century scientific revolutions: Relativity and Quantum Mechanics. These revolutions showed us that the above partitioning was just a temporary way of organizing explanations. Once you properly include the new ideas into our scientific thinking, these subjects are seen to be not isolated; they all flow from the same deep physical principles.

Next time we will begin talking about these revolutions. We will see they were not only critical in realizing Newton’s dream, but are also the key players in the current drama associated with the Higgs Boson.

• What is the Higgs boson?

• Why was it so hard to find?

• Are we done now that we have found it ?

• Why look for it in the first place?

In today’s post we are going to begin to address: Why look for it in first place?

We will start with the basic notion of a scientific explanation: complex natural phenomena — things we observe in our everyday lives — can be explained by simpler underlying concepts. The Greeks had naive versions of this (e.g.: that everything is made of earth, wind, fire, and water, or Platonic solids). We now know that these ideas were deeply flawed, but nevertheless they had this core notion of an explanation, reducing complex things to simpler concepts. However, the notion of scientific explanation really came to life with Newton.

In his amazing work, the Principia, Newton developed modern science. This work had several major breakthroughs: he showed us that mathematics is the language scientific explanations should be written in, he invented a new branch of mathematics to do it, and he spelled out — for the first time — physical laws in this language: the laws of motion and of gravity. This is what Newton’s famous work is remembered for. However, something that is often overlooked — and I think was his biggest advance of all — is what I refer to as “Newton’s Dream”.

I will use cartoons to convey what I mean by Newton’s dream. If there is some higher-level concept (A) that has a scientific explanation according to a law or a simpler idea (B), I’ll indicate the relationship with an arrow; the arrow denotes scientific explanation.

What Newton gave us in the Principia is sketched below. He showed how planetary motion could be described by his laws, he explained how projectiles move on Earth, and described the nature and behaviour of tides.

What is striking is that these three phenomena — which look totally different from one another — are explained by the same underlying concept or idea. Motion of points of light in the heavens, how high the water is, and how apples fall from trees, all seem completely unrelated. Newton showed that the underlying scientific explanation for all three was the same. He goes on to speculate that this can be extended to the rest of what we see in the world.

“I wish we could derive the rest of the phænomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces ...” - Newton (Preface to the Principia)

This is what I refer to as Newton’s Dream: to understand all of nature in terms of simple (mathematical) principles. Of course, Newton was very far from achieving it, but this is the first time you clearly see this aspiration expressed in science.

We will pick up here next time with the realization of Newton’s dream and with what I think has been our greatest scientific discovery of all.

The discovery was announced nearly fourteen years ago and it made a big splash in the press. It ran on the front page of the New York Times and The Economist, and shortly afterward, was awarded the Nobel Prize in Physics. There was a lot of hype at the time.

But if you look past the headlines at what it actually took to discover the Higgs boson, it’s even more impressive. This was not discovered in a small lab in the basement of a university. It took a massive endeavor: the Large Hadron Collider, located outside Geneva, Switzerland. The ring you see in aerial images is larger than an international airport. The idea is that you circulate groups of protons around that ring in each direction, accelerate them to nearly the speed of light, and make them to collide at certain points along the ring. Surrounding those collision points are enormous, sophisticated detectors — think fancy digital cameras made of custom electronics — that take 3D pictures of the collisions. The detectors themselves are the size of apartment buildings.

In numbers, the scale is equally impressive. It took more than 10,000 scientists and engineers, from over 85 countries, working for two to three decades. A 27-kilometer circumference accelerator. Protons moving at 99.9999997% of the speed of light -- as fast as we were able to get them. To discover the Higgs, we had to collide a billion protons per second for two years. The detectors operated at 40 megahertz — which means they were taking their 3D pictures 40 million times per second — and generated about 80 terabytes of data per second. That’s roughly ten times the information in the Library of Congress every second, more data than is handled by big tech companies like Google or Facebook. As you can imagine, something like this is not cheap; the total budget was on the order of $10 billion, not counting the salaries of the people who built and operated everything. And one more number that doesn’t get talked about, but that will actually be important to our story: the salary of the physicist who operates and works on these detectors is much, much less than the salary of a banker or engineer who, in many cases, is doing very similar work. That’s a striking fact that also requires some explanation.

So this is what it took to discover the Higgs boson, and it immediately raises some obvious questions: What the hell is the Higgs boson in the first place?!? Why did we have to go to such extremes to find it? Why was it so difficult, and why did we have to build such large detectors, collect so much data, and so on? Given that it was so hard, why is it worth doing at all? Why look for the Higgs boson in the first place? And now that we’ve found it, are we done?

The whole point of this blog series is to answer those questions — and as we will see, there are many different layers to each answer. We will start with partial answers and build up as we go.