Speed of Light and Time

Question

I'm an amateur and this is my first question here, I'm trying to formulate question about a general representation I have in mind after trying to grasp the idea of relativity and the concept of space-time.

We always talk about the "speed of light", but it's a bit of a misuse of terminology, since we should really talk about "speed of electromagnetic radiations (EMRs)".

Moreover, we recently confirmed that gravitational waves, despite not being of the same nature as EMRs, travel at the same "speed of light".

Considering that, according to relativity, an object travelling at the speed of light would not experience time passing, and that it doesn't seem to make sense to envision travelling faster than the speed of light,

Would it not be natural to consider the "speed of light" as being the "speed of time", or, let's say the speed at which the present propagates through space ?

This way the speed of light and gravitational waves would be actually instantaneous, or at least as much instantaneous as the universe can be, and each point of the universe would "communicate" with the other points at the "speed of light".

Usually when trying to [in]validate this idea by reading other questions or other sources, I find complex explanations that do not really help me evaluate the correctness of the broad model I have in mind.

I do not know if this is something that seems quite obvious to everyone already, but I couldn't find it expressed this way, and this mental picture really makes sense to me. If it does not correspond to our current state of understanding, could you give me some clue of where my formulation does not fit reality ?

Answer 1

If your question is simply about terminology, it's called "speed of light" because light was the first thing people knew of that travels at that speed. It is the speed of massless particles or field disturbances. It is also the speed of causality, i.e. the maximum speed at which any event can affect anything else. See the concept of "light cone."

We could name the speed of light anything, but that will not change what it is.

Answer 2

The word "speed" has a perfectly well established meaning: It is the distance an object travels divided by the time it takes to travel that distance.

It is always permissible, but rarely a good idea, to take a word with a perfectly well-established meaning and give it some other meaning as well.

So yes, you can choose to use the word "speed" this way. You can also choose to call a bluebird a giraffe. I do not recommend it.

Answer 3

One of the fundamental features of relativity is that time is relative, just as space is relative. What "here" means differs between observers, and one observers "here" can appear from another observer's frame of reference to change over time (e.g. the "here" of a passenger sitting on a train is not a single place according to a person on the ground). Similarly "now" is relative, and different observers have different ideas of what things happen "at the same time". This is called the relativity of simultaneity and is very important in resolving many apparent paradoxes of relativity.

Given that time is relative, there really isn't any well defined notion of "the speed of time". Indeed, it's better not to think of time as passing at all. It's probably more useful to think of time as a dimension (like x, y, z) through which objects pass. Different observers may choose different directions in 4 dimensional spacetime for their t, x, y, and z axes.

Answer 4

I want to add something to the different responses you already got. I want to mention that the term you tried to use, that $c$ is the "speed of time", actually has an interesting sense in which it can be said to be true:

Whereas in ordinary mechanics one works with a velocity vector, in relativity one works with something called a four-velocity. This is a four-vector in 4 dimensions, space and time. The magnitude of this four-velocity is always $c$. This means that if an object is at rest in space, it moves at speed c through time. If the object has some velocity in space, it moves slower through time (so in total the magnitude of the 4-velocity remains $c$), which is "time dilation". All of this is of course a gross over-simplification, but it provides a sense in which $c$ is a "speed of time" - the speed that time passes for an object at rest.

Answer 5

Moreover, we recently confirmed that gravitational waves, despite not being of the same nature as EMRs, travel at the same "speed of light".

Things like these makes some of us want to go beyond "speed of electromagnetic radiation in vacuum" to "universal speed limit", or better, (natural) "spacetime conversion factor". In reality, that we even speak of the speed of light at all, is a consequence of us having defined SI units before we knew about the Special Theory of Relativity. If we moved towards natural units, it would not be the concept to talk about.

and that it doesn't seem to make sense to envision travelling faster than the speed of light

Curiously, SR does not actually forbid this. For example, we speak of the expansion of the universe giving us the illusion that some stuff are exiting the finite observable range of our universe at faster than light. It is also somewhat common, in the rare case that time is allowed at the university level, to cover the consequences of tachyons going faster than light, and how that is connected to anti-particles. SR only says that you cannot accelerate a slow thing onto the universal speed limit, and you cannot decelerate a tachyon downwards onto the universal speed limit. We simply do not have a tachyon on our hands to play with.

Would it not be natural to consider the "speed of light" as being the "speed of time", or, let's say the speed at which the present propagates through space?

What you are thinking of is very clearly a time slice moving forward in time. This is to do with a frame of reference, and very little to do with spacetime (and of time) at all. As the other answers have already pointed out, the standard reference with which you measure out a standard thickness of this time slice propagating, is merely convention, and not at all selected by our universe.

This way the speed of light and gravitational waves would be actually instantaneous

No, that is not how any of these works. What you should be doing is to use a suitable observer's time and space measurements, and deduce that light and gravity waves would have a spacetime interval of zero, i.e. they would find an elapsed time in their own proper frame of reference, to be zero.

That is, the light from the Sun takes 8 minutes to come to Earth, and while other observers will disagree with this value, what they can all do and agree, is that in the Sun's frame of reference, the time it takes from the light to get from the Sun to Earth is 8 minutes. This is why we call it proper time. The proper time of the light itself is zero, but that just makes for a complication.

Under no circumstance can you consider the propagation of light waves or gravitational waves as instantaneous.

Answer 6

A speed through time should measure the rate of the passage of time with respect to some parameter, so it better have dimensions of 'unit time per unit something else'. $c$ does not have those dimensions.

The notion of 'speed through time' of some object that makes the most sense to me is $\frac{\text{d}\tau}{\text{d}t} = \frac1{\gamma}$, which expresses the rate of change of its proper time $\tau$ with respect to the time $t$ of an observer. In other words, it measures the relative rate of the same type of physical process (such as the decay of a muon) between the 2 reference frames. This is of course relative and whichever observer you ask will say the other one is slower. Also an observer will always move at 1 second per second in their own frame.

I should point out that this only makes sense for an object on a timelike trajectory; and a lightspeed object does not have a concept of proper time since no physical processes take place on its trajectory to use as a clock. You can't associate a speed through time to light.