Original work. Sept 2009. Revision 1.0

Revision 1.1 : added an alternate explanation for constant speed of light. 

For many years, we have wondered if there is a way to travel faster than the speed of light. Alas, not only can we not do that, we cannot even send a signal faster than light. To do so would allow us to see what will happen before it happens. At a non-quantum scale, cause always precedes effect.

Rest mass:

The traditional way to define rest-mass is as stated by Galileo and Newton. They defined mass as that property of a body that governs its acceleration when acted on by a force.

Particles like a proton or electron have a non-zero rest-mass. For example, the rest-mass of all electrons is 9.10938188 x 10^-31 Kilograms, and all electrons have exactly the same mass. Rest mass is an intrinsic property of the object.

A photon however, has no rest mass and yet it is the carrier for the electromagnetic force. How then, can something with no mass take part in a physical interaction like a solar-cell? If a photon has no mass, how is it able to knock electrons about and make an electric current? You will read, no doubt that light from a distant planet is bent by a gravitational field. How can it be influenced by a gravitational field if it has no mass?

I am going to start this with the traditional explanation of relativistic mass, but try to read this as just one of a possible number of explanations - not that it is wrong, but just with the mind that although this is a common explanation, it is not the only way to look at things. At the end of this section I will present another approach on how to understand the constant speed of light.

Surprisingly, confusion about mass is seldom explained clearly in elementary texts, and taken for granted in more advanced treatments.

Einstein's famous E=Mc² equation shows that mass and energy are related. We know that a photon has energy, and we know that it moves at 299 792 458 meters every second. This has the symbol "c".

By rearranging Einstein's equation into M = E/c² we see that M cannot be zero because c is a constant, and a photon has energy.

Here is the source of confusion. Mostly, you hear this equation described as the mass energy equivalence equation. If it is thought of as the relativistic mass energy equivalence equation then it makes it clear that something other than the Galilean definition of mass is being used.

Just to add a little more confusion back (you don't get anything for nothing), even the use of the term relativistic mass has been controversial. See this university page for more information.

E=Mc² says that the relativistic mass of an object may be quantified in units of energy and vice versa. The conversion factor is c². As energy is added to a system, that system's mass is increased. This implies that a stone would weigh more on Earth if it is heated up, and that is true. However, the difference would be insignificant.

Rest-mass is a property of an object which is measured to be the same value no matter what your frame of reference. Relativistic mass is not measured the same for all frames of reference. It comes into play when an object is moving, and is added to the rest-mass. At low speeds, relativistic mass has little effect, but at speeds approaching c, the effect is completely overwhelming.

An object with rest-mass that is moving near the speed of light - as in the case of an electron in a cathode-ray tube requires the rest-mass plus the relativistic mass of the electron to be used in ballistic calculations.

Many physicists prefer to avoid the confusion over mass by using only rest-mass, and noting that this is a property of the object itself which is measured to be invariant. That is, it has the same value to all observers regardless of their speed. Any energy added to a system is described in other terms than mass - such as momentum. This removes the confusion somewhat, but in popular texts, the term relativistic and rest-mass are here to stay.

I promised an alternate way to look at the constancy of light. Here it is:

The fact that a photon has no rest-mass means that it cannot be accelerated. Therefore is has to travel at c. So you cannot BOUNCE a photon, or 'give it a nudge', and if you do something to add more energy to it then its frequency changes but not its speed. For example, if you rush towards a photon, then it blue-shifts which means, for your frame of reference, it is a higher energy, and thus is more energetic. Conversely, if you back away from a photon then it red-shifts and looks like it has a lower frequency and less energy. When you make a torch shine, then you are creating a fresh photon which leave the torch at c until it bumps into something at which point it is absorbed. In transparent mediums like glass and air etc, the photons are mostly absorbed and re-emitted, usually with a different direction (scattering), perhaps with a significant colour when some frequencies are absorbed more easily. But in free space, we can think of the photon that you created as zipping off into space at c.

Let's stand on the ground and do this in a thought experiment. Stand on a moving walkway with a torch pointing forward. The photons are still leaving the torch at c. Now speed up the walkway incrementally for a moment and fall back to a constant, but greater velocity (relative to the people not on the walkway). The photons still leave the torch at c. Now imagine everything around you except the walkway to fade away so that you cannot detect anything except you, your walkway, the torch, and the light beam. Everything looks exactly as it did when you where stood firmly on the ground. You can't tell in your inertial frame whether you are moving or not. Now the walkway accelerates again - just a little. You can tell that happens because momentarily, you feel a as if a gravitational pull acted on your back. But when it settles down, your torch is still creating photons at c, and you can't tell whether you are moving or not. You can get 'boosted ' like this forever, and the torch still creates photons that leave at c. Time and motion look normal to you at all times that you are traveling at constant velocity. The people next to the walkway view a different scene though. They see you periodically accelerating towards the speed of light (in their frame of reference), but never actually reaching it. Your movements appear to them to slow down progressively.

The relativistic mass that we were talking of earlier is only of any importance to the people who are watching you on the walkway. Furthermore, if there were other walkways with people traveling on them and they could see you, their impression of you and your torch would be different in each case. But inside your inertial frame, everything is just sweet.

The tough question is "Why does light travel at a constant speed?". No one really knows. The speed of light may be expressed in terms of two other constants, but that does not really help you answer the question. The converse question is somewhat more revealing which is, "How could light travel at ANY speed?" If you heard that light must travel at a constant speed no matter the frame of reference and find it hard to swallow, then the consequences of imagining it to travel at any speed is preposterous. This would imply allowing to travel infinitely fast, or send a signal infinitely fast which is ridiculous in the extreme. Not only is the the very term, infinitely fast nonsensical, all you need to do is look at the night sky and ask, "If light traveled infinitely fast, then why am I not burned to a crisp from all the light arriving at me in zero time, and how silly is that anyway, and also why can I see the stars at all?". Everything that ever happened, and ever will happen would have already happened in literally no time. In this thought experiment, where light is allowed to travel at any speed, including infinite speed, there is no time, there are no events, there is no matter, there is nothing. So light MUST have a speed limit.

Since a photon has no rest mass it can ONLY go at c (the speed of light), no faster, no slower. It cannot accelerate or decelerate. It can only be absorbed, or emitted upon interaction with an obstacle. I say this while also mindful of Feynman's highly successful theories about virtual particles, and what I am referring to is the average result of the speeds and trajectories of these virtual particles. I also say this knowing that a light-beam can be slowed down in a special gas at low temperatures to become stationary. However, this is an aggregate phenomenon where the light beam is contained in a small area. All the individual photons are still moving at c.

Remember: When energy is added to an object, that object has more relativistic mass.

To move an object, you must add energy to it. Even at low speeds, to accelerate an object, you must add more energy this moment than was added the previous moment.

Force = Mass X Acceleration

Velocity is meters per second.

Acceleration is the rate of change of velocity, and is therefore in units of (meters per second) per second.

But as an object approaches relativistic speeds compared to an observer in an inertial frame, it gains significantly more energy, and this compounds the problem of accelerating it further.  It's a problem which gets out of hand the faster you go, with the ultimate conclusion that an infinite energy would be required to accelerate a mass to c. Since infinite energy is not available, nothing with non-zero rest-mass can travel as fast as light.

An object is either massless and is emitted at the speed of light, or it has some rest mass and cannot reach or exceed the speed of light.

A Tachyon is a hypothetical particle with "imaginary" mass suffering the same kind of problem. It cannot be decelerated to the speed of light. These things appear in some serious theoretical frameworks - like the limited and outdated but interesting bosonic string theory which is a 26-dimensional theoretic playground. But because they cannot cross that same light speed barrier, we could not access even a localised Tachyon particle to transmit a signal faster than light. In any case, in the theories in which they present, they are highly unstable, and tend to ring alarm bells for the theory in play.

So all those Sci-Fi movies that use "Tachyon beams" to communicate across vast spaces are really pushing the envelope as it were.

Bending space is fundamental to General Relativity (GR), and theoretically might be exploited to join two distant parts of the universe by folding space and punching a hole into it. But the amount of energy postulated to do such a thing is mind-blowing. Whether humans could ever do such a thing is very speculative. But even if this were possible, and we could join two distant regions of space though a wormhole or whatever you like to call it, we would not be required to exceed the speed of light to move through it.

We said earlier, that the dark night sky is a good reason to conclude that light has a speed limit. But it does not explain why the universe is gradually heating up to extreme limits, and therefore glowing at night as bright as our sun in the daytime. You see, since we strongly feel that there are either infinite stars out there, or certainly a mind-numbing large amount, and they are very very old. Anywhere you look in the night sky should coincide with billions of stars, and be very bright. "Space itself is expanding" and "Light takes significant time to get to us from the distance of the stars". This explains why most of the night sky is very dim despite the enormous number of stars beyond what we can see. Importantly, this also demands that the universe is not infinitely old. If it were, then even though light has a speed limit, there would be enough time for the night sky to glow brightly through the accumulation of photons from countless stars even though they are very far away.

Yes!

Since space itself is expanding, two objects moving in opposite directions at near the speed of light could be separating faster than light could be sent between them. Faster than light signaling is not possible even in this mind-boggling scenario.

In fact, the traditional big-bang theory suffers some issues with observations of deep space. The cosmic background radiation is so incredibly uniform, that we theorize that the very first instant of the big-bang was followed by an incredible expansion rate.

Using the traditional theory of the big-bang, energy and information would have to be transported at about 100 times the speed of light in order to achieve uniformity, 300,000 years after the big bang. We actually observe the expansion of space still today, albeit at a much slower pace, but we never observe faster than light signaling. The cosmic background radiation does have some incredibly tiny fluctuations. If, instead of surmising that light traveled 100 times faster an instant after the big-bang, we modify the big bang theory to include a tremendous but brief inflation period, the level of uniformity is nicely explained, and the tiny fluctuations are explained.

Yet again, this is evidence that light has a speed limit.

Imagine two dots on a balloon. An ant tries to run from one to another as fast as it can. But someone blows up the balloon so fast that the dots move apart faster than the ant can run. If the ant's top-speed on the balloon was analogous to light-speed in our universe, then these dots move faster than ant speed, and we can see how expanding space can separate objects faster than the speed of light.

Now imagine a small balloon with a fluid surface, and suspended in the surface is a powder. It might be unevenly distributed, or concentrated on one spot - it does not matter much as the starting conditions are not particularly chosen. Given enough time, the powder might become uniformly distributed around the whole balloon, but this might take weeks or months, or not happen at all. Now imagine the experience of one ant at some point in the unevenly distributed powder. Someone comes along and blows the balloon up to the size of a large ocean liner so fast that it suddenly appears almost as a flat surface to the ant. All the powder in that particular area would, by virtue of the rapid expansion of that local area appear to the ant to be almost perfectly evenly distributed. This is a rough analogy to the observed distribution of cosmic background radiation today. The ant, like us, sees a world which appears special even though the starting conditions were not particularly conditioned.