Student blog: Quantum Physics II – Quantum Theories

Quantum theories of systems such as atoms were formulated in the 1920s by Heisenberg, Schrödinger, and Dirac. 

The Uncertainty Principle

The famous Uncertainty Principle states that you can never know the exact positions and speed of an object in the quantum universe. This is why… 

The uncertainty principle exists because everything in the universe behaves as a particleand wave at the same time. 

Particles exist in a single place at any instant in time. A particle can be 100% and 0% anywhere else. On the other hand, waves are disturbances spread out in space (like ripples covering the surface of a pond). We can clearly identify features of the wave pattern, such as the wavelength, though we cannot assign it a single position – it has a measurable probability of being anywhere. 

Wavelength is extremely important in quantum physics as an object’s wavelength is related to its momentum:

Momentum = mass x velocity

A fast-moving object has lots of moment, as does a heavy object even if it’s not moving much:

50g   x   5m/s    = 250 kg•m/s

5g     x  50 m/s = 250 kg•m/s

It should also be noted that wavelength and momentum are related: 

Short wavelength means lots of momentum (take two objects of the same mass, if one has a shorter wavelength, it, in turn, has a higher velocity and so a higher momentum. An example of this is the visible light spectrum, red light has a longer wavelength and so travels slower as opposed to violet which has a shorter wavelength and so travels faster). 

Therefore, we don’t notice the wave nature of everyday objects. 

However, wavelengths are far too small to ever be measured. Although, atoms or electrons can have wavelengths big enough to be measured in physics experiments. If we have a pure wave, we can measure its wavelength and so its momentum. BUT it has no position. Consequently, we can know a particle’s position very well, but it does not have a wavelength. Meaning, we do not know its momentum. 

To get a particle with both position and momentum, we need to mix the two concepts. This is done by combining the waves with the different wavelengths – giving the quantum object a possibility of having different momenta. This is because when two waves are added, there are places where the two peaks line up – making a bigger wave. In other places, the peaks and troughs cancel each other out – resulting in regions of waves separated by regions of nothing. 

As you add more waves, the nothing regions get bigger and the wavy regions narrower. This is called constructive interference

By adding more waves, there is a clear wavelength in one small region. That is a quantum object, with both wave and particle nature. However, to get there we had to lose certaintyabout position and momentum. 

To reduce position uncertainty, you need to add more waves, which means a bigger momentum uncertainty.

To reduce momentum uncertainty, you need larger wavy regions, which means a bigger position uncertainty. That is the uncertainty principle, you can never know both the exact position and speed of an object. 

String Theory

In basic terms, string theory is a theory of the fundamentals of everything in the universe. It has not been proven true however it is still a widely believed and accepted theory.

There are subatomic particles even smaller than protons and neutrons which the protons and neutrons themselves are made up of, known as quarks and gluons. String theory suggests that inside these quarks there are tiny vibrating strings of energy that make up the quarks themselves.

Schrödinger’s Cat

Erwin Schrödinger is a founder of quantum physics; however, he is most well known for his thought experiment. 

He imagined placing a cat in a sealed box with a device that had a 50% chance of killing the cat in the next hour. This is linked to radioactivity, as the cat is placed in a box with a radioactive substance that could explode or release a harmful poison as it decays. At the end of the hour, what is the state of the cat? 

You would say that using logic it is either alive or dead. However, Schrödinger realised that according to quantum physics, the cat is both simultaneously, only when the box is opened is the cat either alive or dead. 

The Universe in a Nutshell

Has the universe existed for an infinite time?

Until the early 20th century, it was believed that the Universe had existed for an infinite time. But if stars had been radiating for an infinite time, they would have heated the Universe to their temperature. And at night, the whole sky would be as bright as the sun – since the Universe is so vast, every line of sight would end either on a star or on a cloud of gas – known as a nebula – that had been heated up until it was as hot as the stars. 

However, we can all agree that the sky at night is dark. This is very important because it implies the Universe cannot have existed forever. Something must have happened in the past to make the stars light up a finite time ago, and so the light from very distant stars had not had time to reach us yet. This explains why the sky at night isn’t glowing in every direction. 

Most people believed that the Universe had been created but only a few thousand years ago. However, observations by Edwin Hubble, in 1923, showed that faint patches in the sky were galaxies, made up of many stars like our sun but at a great distance. For them to appear so small and faint, the distances had to be so great that light from the would have taken millions or even billions of years to reach us. This concluded that the Universe could not have been formed just a few thousand years ago. 

The Doppler Effect

The Doppler effect is the relationship between speed and wavelength, we experience it on an everyday basis. 

Imagine the horn of a truck passing by you, as it approaches you, the sound waves are closer together, so they are at a higher frequency meaning a higher pitch. As the vehicle moves away, the waves spread out (are further from apart) and so you hear them from a lower frequency, a lower pitch. 

That is the Doppler effect. 

By definition, it is the change in frequency of a wave about an observer who is moving relative to the wave source.

The same concept applies to light. As the light source gets closer, the frequency increases. Just like how frequency in sound is pitch, frequency in light is its colour – higher frequency light waves are towards the violet end of the spectrum whereas low frequency light waves are towards the red end of the spectrum. This relates to redshift.

As we all know, thanks to Edwin Hubble, galaxies and everything in the universe is moving away from everything else at a constant speed. This means that light waves are having to travel further distances to reach us, as a result, the waves are stretched towards the red end of the spectrum. This is redshift. 

By analysing the light from other galaxies, you can measure whether they are moving towards or away from us because of the Doppler effect. Using this, astronomers discovered that nearly all galaxies are moving away and that the farther they are from us, the faster they are moving away. Hubble noticed that this meant that every galaxy is moving away from every other galaxy. The Universe is expanding.

If galaxies are constantly moving further and further apart, at some point in the past they would have been very close together. This proves the Big Band theory: at some point, all the mass in the Universe was compacted into a very small ball. We estimate that this point must have been 10-15 billion years ago. 

The universe began in a Big Bang, a point where the whole Universe, and everything in it, was scrunched into a single point of infinite density. Einstein’s general theory of relativity would have broken down at this point because it does not incorporate the uncertainty principle. 

Image from Wikimedia Commons

Richard Feynman

Richard Feynman challenged the basic assumption that each particle has one particular history. Instead, he suggested that particles travel from one location to another along every possible path through spacetime. With each trajectory, Feynman associated two numbers, one for the size – the amplitude – of a wave and one for its phase – whether it is a crest or trough. You find the probability of a particle going from A to B by adding up the waves associated with every possible path that passes through A and B. 

Nevertheless, in the everyday world, as we see it objects follow a single path between their starting point and endpoint. This agrees with Feynman’s multiple history idea because for large objects his rule for assigning numbers to each path ensures that all paths but one cancel out when they are combined. Only one of the infinity of paths matters as far as the motion of macroscopic objects (objects that we can see in plain sight) is concerned, and this trajectory is precisely the one emerging from Newton’s classical laws of motion.

Scientists are now working to combine Einstein’s general theory of relativity and Feynman’s idea of multiple histories into a complete unified theory, known as the Theory of Everything, that will describe everything that happens in the universe. The theory will allow us to calculate how the universe will develop if we know how the histories started. But the theory will not in itself tell us how the universe began or what its initial state was. For that, we need what are called boundary conditions, rules that tell us what happened on the frontiers of the universe, the edges of space and time. 

If the frontier of the universe was just a normal point of space and time, we could go past it and claim the territory beyond as part of the universe. On the other hand, if the boundary of the universe was at a jagged edge where space and time were scrunched up and the density was infinite, it would be very difficult to define meaningful boundary conditions. 

However, there is a third possibility. Maybe the universe has no boundary in space and time. At first sight, this seems to directly contradict theories such as that of the Big Bang that the universe must have had a beginning, a boundary time. However, there is another kind of time, known as imaginary time, that is at right angles to the ordinary real-time that we feel going by. The history of the universe in real time determines its history in imaginary time, and vice versa, although the two kinds of history can be very different. In particular, the universe does not need to have a beginning or end in imaginary time – imaginary time behaves just like another direction in space. As a result, the histories of the universe in imaginary time can be thought of as curved surfaces such as a ball or a plane. If the histories of the universe went off to infinity like a plane, you would have the problem of explaining what the boundary conditions were at infinity. However, this can be avoided if the histories of the universe in imaginary time are closed surfaces such as the surface of the Earth, the Earth doesn’t have any boundaries or edges. 

The Boundary Condition

The boundary proposal is based on Feynman’s multiple history idea, but the history of a particle in Feynman’s sum is replaced by a complete spacetime that represents the history of the entire universe. The no boundary condition is imaginary time. In other words, the boundary condition of the universe is that it has no boundary

As well as matter, the universe may contain vacuum energy, energy that is present even in empty space. By Einstein’s equation E = mc², this vacuum energy has mass. Meaning, that it has a gravitational effect on the expansion of the universe. Despite that, the effect of vacuum energy is the opposite of that of matter. Matter causes the expansion to slow down and can eventually stop and reverse it. On the other hand, vacuum energy acts just like the cosmological constant that Einstein added to his original equations. 

Written by Dinuli, a Year 10 Student at Harris Academy Bromley

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