# Let's Talk Physics

A stochasticly updated blog about interesting topics in Physics & Astronomy

# The Speed of Light

A few years ago, researchers in CERN announced that they had found a particle which travels faster than light. For the next few months, physicists separated into 2 camps. Camp A said that the results were wrong, and the experiment had been done wrong, as nothing can travel faster than light. Camp B said “Ok, maybe the results are wrong, but what if they aren’t? What if there’s new physics here?” In the end, it turned out the clocks used for the experiment hadn’t been set right (or something similar to this), and the speed of light remained this maximum speed of anything ever. But why is that, and what consequences does it have for us now, and what would happen if we ever traveled faster than it?

The speed of light is 299,792 km/s, or more formally written as just c. So what does it mean to travel at this speed? Firstly, light is not a continuous beam of energy, as most people believe. Light travels as tiny amounts of energy, called photons, and these photons, which aren’t made up of mass, travel at a speed of c.

Here is an example of 3 photons of light

So what happens when an object with mass starts moving close to the speed of light? Intuitively, you would say that if an object is accelerating with nothing to stop it, its speed will keep on getting larger and larger, and it will go faster than light. Sadly, physics doesn’t obey intuitiveness when you’re dealing with speeds close to c. When an object gets close to c, and it “accelerates”, rather than getting more velocity, it gets more massive!

Energy and mass are equivalent. By saying that the average human is 72kg, what we’re actually saying is if that person’s mass were converted into energy, it would be the same as $6.471\times10^{18} Joules$  (by using Einstein’s most famous equation $E=mc^2$).  Another relation I’m going to use here is the idea of Kinetic Energy (or K.E. ). K.E. is the energy an object has because it has a velocity. Below is a graph showing how the 2 are related.

Kinetic Energy increases with velocity

So, from the above, we can conclude one thing – the energy of a body can increase in 2 ways. Firstly, either its velocity can increase, or its mass can increase. For everyday objects, like cars and airplanes, the velocity is the quantity that increases. But when an object starts travelling close to c, things change, and the energy is added to the system by the mass of the object increasing. Which spells bad news if you’re trying to lose weight and decide to take a trip to your nearest star by traveling close to c.

Now for some other funky effects of travelling close to the speed of light. Most of us know time as being pretty constant – a second for me is the same as a second for you. But close to c, this no longer applies, and time becomes completely relative. The faster someone travels, the slower time passes for them. This leads us onto the twin paradox. Take 2 twins. Leave one on Earth (say Bob) and put the other (say Tim) in a spaceship to orbit the Earth for a while at a speed close to c. When Tim finally comes home, he’ll find Bob to be a lot older than he is, and this is because time passed slower for Tim while he was in the spaceship – kind of weird, right?

So, can things actually go faster than the speed of light? Well, we know that something that has mass most certainly can’t – if it gets close to the speed of light, the object will get more massive rather than actually get faster. This is seen everyday in CERN at the Large Hadron Collider. A proton moving very slowly has a mass of about $1.7\times10^{-27} kg$. However, at CERN, protons travel very close to c, and their mass increases to $1.24\times10^{-23} kg$. That’s an increase in mass of about 7,460! And the more energy is given to these protons, the more massive they’ll get. Now, we also know that photons travel at exactly c, and they can do this because they have no mass – they are pure energy. So, logically, something that travels faster than c would have negative mass right? Wait….what? What the hell does negative mass mean?

A proton moving at normal speeds. (Click to enlarge)

A proton moving close to c. Not even once. (Click to enlarge)

The concept of “negative mass” is best explained through use of light cone diagram. Below is a graph where the x axis represents a position in space. The y axis represents time (with the positive y being the future and the negative y being the past). The crossing of the x and y axis represents where you stand right now. The cones which are coming out represent the position in space you would go to if you were travelling at c. Hence, you can travel anywhere within your future light cone, and the past light cone represents every possible way which you could have used to arrive where you are. If you were a photon of light, you would follow the cone.

A light cone. Anywhere inside the future light cone is where you can now go, while the past light cone is how you got here

Everything outside of the light cone represents something that could travel faster than light – a particle of negative mass. This region is called Elsewhere. Theoretically, these particles exist, and have the strange power of being able to travel backwards in time (like the famed Tachyons from Star Trek). So, hypothetically, you can travel faster than light – you just need to have negative mass to do it.

I'm a PhD student with the Departments of Physics in University College Cork, Ireland and University of Notre Dame, Indiana. I want to try and bring astrophysics to the public, and also would like world domination. But that's a story for another day.

### 4 comments on “The Speed of Light”

1. Thomas Kelly
March 4, 2013

An interesting article. I have a few small comments.

Mass is a tricky thing, because it is a word that can mean two different things. In the above article, you discuss two very different concepts of mass: the increase in mass as a particle speeds up, and the idea that a photon is massless. The former references “relativistic mass”, while the latter references “rest mass” or just “mass” in modern contexts. These are very different quantities. For example, if we consider relativistic mass, then photons actually do have mass of an amount equal to their energy. If we consider rest mass, then a photon is massless, but the mass of a proton in the LHC doesn’t increase as the protons are accelerated. Instead, it is their momentum that increases.

So what does it mean to say a photon is massless? It wouldn’t be quite correct to call photons pure energy. Energy is a property of a thing, rather than a thing itself, and therefore pure energy wouldn’t exist. Instead, I would say photons are expressions of the electromagnetic field. They have momentum and energy as properties. In fact, it is because they have the same amount of energy as they have momentum that we call them massless. (Mass, to a physicist, is basically a measure of the difference between a particle’s energy and momentum.)

Finally, and this is just a small point, the mass of a particle wouldn’t have to be negative to travel faster than light. Instead, it would have to be imaginary.

• irishphysicist
March 4, 2013

Hey Thomas,

Firstly thanks for the comment, it’s always nice to get feedback on this.

Secondly, thanks for picking up on the whole “calling a photon massless” part of this. I was incredibly vague on the topic, but you covered it very well here (and I probably used some very dirty phrases that, as a physicist, I should be ashamed of 😛 ).

Also, agreed with the whole “imaginary” ass opposed to “negative” mass idea. Will update the post accordingly.

Mark

2. M J Murcott
June 21, 2013

Does a photon of light have mass or can energy and mass be interchanged – http://youtu.be/B1DCP4C4MnY

• jdriordan
June 26, 2013

Thank you for posting your video. I’m afraid your idea venture into the world of “crank physics” and while interesting, and historically relevant, are demonstrably false.

Waves and particles are models, way of (mathemically) describing phenomena. Photons (“photon of light” is redundant) are not accurately described by either model, however accurate predictions can be made by both.

Photons do indeed have mass in one sense, this is known as “relativistic mass” and it means that gravity affects photons just as it affects matter. The sense in which you mean mass, “rest mass”, is equal to relativistic mass for stationary particles (and approximately equal for those moving at speeds you’re ever likely to encounter) but photons are never found at rest, indeed they move (in general relativity) at the speed of light always, and so while it is true that their rest mass is zero, it is somewhat a moot point.

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