Tag Archives: Relativity

Simpler overviews

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This thread gives presentations that are simpler and necessarily less complete overviews of the subjects of main articles. As such, they may not contain enough information to be quite convincing. Sorry about that. These are sometimes counter-intuitive subjects.

So we suggest that you start with the full version and only come here in case of need or, maybe, to review. Appropriate links exist in the main articles.

We will start with the Big Three theories of physics.

Thermodynamics

Thermodynamics is the branch of physics which started out talking about heat energy, in the early days of steam engines. Then other forms of energy, like electromagnetic or nuclear energy, came up and were included, so today it is the general theory of energy. We will be talking a lot about energy, so thermodynamics is important to us.

Thermodynamics posits three laws:

  1. The energy of the universe does not change; it is always conserved.
  2. In a physical process, the entropy of the universe always increases.
  3. The entropy of a system at a temperature of absolute zero is zero.

Law number one says that energy is always conserved. In fact, like speed limits, this one can be violated provided the perp does not get caught. This happens in Quantum Mechanics and we will look at that shortly. For anything bigger than an atom, though, energy is always conserved.

Law number two says in any process involving transformation of energy, you are probably going to lose some. This is equivalent to saying that the universe goes from a relatively ordered state (such as large plates stacked together, small plates stacked together, no large ones mixed with small ones) to a relatively unordered state (all the plates stacked together in any old order). Take a look at the Entropy entry on the main menu bar for more (easy) details. Most simply put, entropy is a measure of disorder. Nature seeks disorder, and therefore increased entropy. Entropy thus serves to predict which direction a process will take, forwards or backwards in time.

A standard example is the breaking of an egg, in which the egg becomes more disordered and therefore in a state of higher entropy. To do the opposite, for the broken egg to come back together, would require a decrease in entropy. Have you ever seen a broken egg re-form itself?

We are victims of entropy too. We eat food to provide energy to maintain our bodies in their highly ordered state. Whenever metabolism stops, rot sets in and .. we return to unordered dust.

We will use entropy in the following pages to explain why lots of things happen the way they do, rather than the opposite way.

Law number three just gives a base value for entropy measurement. Zero Kelvin is really cold, so cold we have never been able to get there in a laboratory. Precisely, it is -273.15° Celsius or zero Kelvin. We don’t do Fahrenheit.

Maybe you would like to check the full version now. If not, just go on.

Quantum Mechanics

Quantum mechanics is the theory we use to talk about atoms and elementary particles. i.e,  of what happens at very small dimensions, on the order of 10-30 meters or less! On that scale, things are very unusual.

There is no way to make QM intuitive. So here goes…

According to quantum mechanics, what is “out there” is a vast amount of space – not an empty backdrop, but actually something. This space is filled with particles so small that the distance between them is huge compared to their own sizes. Not only that, but these particles are actually waves, or something else which acts sometimes like waves and sometimes like particles. Light sometimes diffracts like waves (think prism) and sometimes leaves traces like particles.

As if that were not bad enough, it is impossible to measure simultaneously where they are and how fast they are moving (or how much energy they possess and when). This last effect is referred to as indeterminacy, or the Uncertainty Principle, one of the more uncomfortable and, simultaneously, fruitful results of the theory. We already have mentioned this exception to the First Law of Thermodynamics.

The three main difficulties most people have with QM are the following:

  1. the so-called wave-particle duality;
  2. the existence of discrete quanta for values of physical parameters;
  3. the Uncertainty Principle;
  4. the Exclusion Principle.

We have already mentioned numbers 1 and 3. Number 2 comes from the math. In fact, QM is a mathematical formalism with an equation one can (try to) solve for any given object of study. In general, the equation only has solutions for certain values of the parameters of the system. These might be the energy or the angular momentum or other things. For an atom, only certain energies are possible. Such allowed values are called quanta.

The Exclusion Principle says that certain particles known as fermions are constrained in such a way that no two of them can occupy the same QM state. Electrons are fermions. So this phenomenon, called the Exclusion Principle, is at the root of solid-state physics and therefore of the existence of transistors and all the technologies dependent thereupon – portable computers, mobile telephones, space exploration and the Internet, just as to mention a few examples. So QM has indeed revolutionized modern life, for the better and for the worse (think of wasteful and dangerous nuclear bomb proliferation).

The exclusion principle is also responsible for the fact that electrons in a collapsing super-dense star cannot all be in the same state, so there is a pressure effectively keeping them from being compressed any further. We will read more about that in the cosmology chapter.

Maybe you would like to check the full version now. If not, just go on.

Relativity

Relativity is not the idea that ‘everything is relative.” It is about relative motion.  The first, or Special Theory of Relativity says that if you are in a moving train and I am standing still outside, we will both use the same equations to describe what is going on, although the values we get may be different. I think you are moving, but if you have just waked up from a deep nap, you may think you are standing still and I am moving. But the oddball thing is that if you and I both measure the speed of light, we will come up with the same value, independently of how fast either of us is moving with respect to the other.

Normally, if you walk along your train car from the back to the front of the train, you will figure you are walking at something like 4 km per hour. But if the train is moving at 100 km per hour, I will see you moving at 104 km per hour. But if it is a beam of light from a laser which you shine down the length of the train, we will both measure the same value, about 300,000 km per hour. Bizarre, non?

The other odd thing of Special Relativity is that time and space are not independent, but go together in what is called space-time. And only massless, objects can travel at the speed of light, like photons, the particles of light.

If a massive object like my sister traveled at high speeds, near the speed of light, it would seem to me that she was getting heavier but thinner (perpendicular to the direction of her motion) and her clock would run more slowly. This includes her bodily clock — her heart. This is the heart of the Twin Paradox. If she takes a very fast spaceship on a joy ride, when she gets back, she will be younger than any hypothetical twin she may have left behind on earth. This has been tested (with high-speed particles) and is definitely true.

The other Relativity theory is called General Relativity. Whereas Special Relativity is the theory of space-time and light, General Relativity is the theory of gravity. GR says that space-time is curved and that it is more curved where gravitational forces are stronger. In fact, gravity is the curvature of space-time. Think of a plane surface with a depression in it. Put a ball on it and the ball will roll into the depression. Try to visualize that in four dimensions (Good luck!) and you’ve got GR.

Please take note: QM, SR and GR are all tested and confirmed theories. They are not hypotheses, they are true — at least for the moment. Any subsequent theory which amends them will have to include or explain their results.

Maybe you would like to check the full version now.

For the moment, I do not see how to simplify the next subject any more than I have already.  So go on to the Standard Model of Elementary Particles.

Relativity

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Special relativity

Just as QM is the theory of the very small, Relativity is the theory of very large dimensions.

As usual, if this page gets to be too much, try the simpler version. This one is recommended, though.

In fact, there are two theories of relativity. The simpler, first one, called Special Relativity (SR), is about space-time, relative movement and the speed of light. It says:

  1. the equations of physics are the same (invariant, in math-physics speak) for all observers who are moving with uniform steady motion relative to each other1Such observers are said to be in inertial systems.;
  2. the speed of light in a vacuum is a constant, the same for all observers.

The first statement, the principle of relativity, means that if someone goes by you in a high-speed train on a straight track, then either you or she can consider herself to be stationary and the other moving. If you have traveled by train, you may have wondered sometimes whether your train was advancing or the one next to you was moving backwards.

The second statement means that if both you and your friend in the train measure the speed of a light beam, you both will find the same answer, about 300,000 km/sec. This is not intuitive.

From these two statements, lots of things follow, including.

  • the equivalence of mass and energy, expressed by everybody’s favorite (and perhaps only) equation, E=mc2;

  • the fact that only bodies without mass can travel at the speed of light;

  • curious distortions like the faster someone is moving relative to us,

    • the heavier she gets,

    • the shorter she gets in the direction of motion and

    • the slower her clock runs, including her body clock, the heart.

This last point is the origin of the famous twin “paradox”. If your twin takes off in a space ship and travels fairly fast compared to the speed of light, then when she gets back to Earth, she will be younger than you, the twin she left behind. Strange, but this has been tested (with particles) and found to be true.

All this comes out of the mathematics for describing relative motion, which is in turn due to the fact that space and time are not independent, but form a four-dimensional “thing” called space-time. What we see as space and time are aspects of space-time and can appear differently for different observers. And they can get mixed up together, especially if you are traveling at high speeds.

General relativity

The other Relativity theory is called General Relativity (GR). Whereas Special Relativity is the theory of space-time and light, General Relativity is the theory of gravity. GR says that space-time is curved and that it is more curved where gravitational forces are stronger. In fact, gravity is the curvature of space-time. Think of a plane surface with a depression in it. Put a ball on it and the ball will roll into the depression. Try to visualize that in four dimensions (Good luck!) and you’ve got GR. Uh, sort-of …

There are also lots of things which follow from GR. One of the more interesting is that gravity can change the direction of light, since light travels through the space deformed by gravity. This and many other predictions have been observed to occur just as GR predicts.

Curiously enough, clocks run slower in a stronger gravitational field. A clock runs faster on top of a high building or in a satellite than it does on the surface of the Earth. For a satellite, this is opposite to the effect of high speeds on fast-moving clocks in SR, which makes them run slower. The two corrections are in opposite directions but do not cancel each other completely, so both must be applied to GPS systems in order for them to function correctly.

More recently, we have discovered that not only is space-time curved, but that space is expanding. This is because a gravitational field exerts not just a force, but a pressure. This pressure is considered to come from a term in the equations of GR called the Cosmological Constant. Unlike the force of gravity, which is always attractive, the pressure can be negative, in which case it is not attractive, but repulsive. It is the outward force of the negative pressure which drives the expansion of space. For the last 7 Gy2Gy means giga-years, or 109 years or 10 billion years., the expansion of space has been accelerating. More about that in the cosmology chapter.

QM and GR — an unhappy marriage

As far as they go, SR and GR are as true to nature as can be detected within their separate domains, and so constitute bodies of knowledge – theories. They must be taken into account practically for the technology of GPS systems.

The problem is that QM does not work on the scale of GR, nor the other way around. This is probably the biggest problem in contemporary physics, the resolution of which is the grail now pursued by theorists.

In summary:

We live in a world where matter sometimes behaves like a particle and sometimes like a wave and where only probabilities can be calculated. All this is taking place in a curved four-dimensional space-time which is expanding at an accelerating rate! And this space is not an empty vacuum, it is something.

Got that?

Now onto the the standard model of elementary particles.

Notes

Notes
↑1 Such observers are said to be in inertial systems.
↑2 Gy means giga-years, or 109 years or 10 billion years.