Faster than the speed of light?

I've heard that nothing can travel faster than the speed of light. Is that actually held to be a scientific truth, and if so what is the basis for that?

The reason I ask, I was watching a video on relativity, and it illustrated a straight-line light beam traveling through space. Superimposed upon the beam was the electromagnetic sine wave that is a part of that light beam. In a way the whole thing looked like a ski boat traveling across a lake, with the skier cutting back and forth across the straight-line path of the boat (wake).

I've skied enough back in the day to know that cutting back and forth across the boat's path makes the skier go at much greater speed than the boat, adding lateral movement to the forward movement. So, I'm wondering that, if the straight-line speed of a light beam is c, then isn't the electromagnetic wave that constantly crisscrosses it going at a speed significantly faster than c?

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Nugatory
Mentor
I've heard that nothing can travel faster than the speed of light. Is that actually held to be a scientific truth, and if so what is the basis for that?
Basically, you start with Einstein's postulates (two very reasonable-sounding and solidly experimentally confirmed assumptions about how the laws of physics behave) and the rest follows from there. You'll find many threads here discussing this in various levels of detail.

The reason I ask, I was watching a video on relativity, and it illustrated a straight-line light beam traveling through space. Superimposed upon the beam was the electromagnetic sine wave that is a part of that light beam. In a way the whole thing looked like a ski boat traveling across a lake, with the skier cutting back and forth across the straight-line path of the boat (wake).
Those pictures are misleading, because the lines representing the electrical and magnetic fields aren't really moving back and forth across the path of the light. We're graphing the strength of the electrical and magnetic field at each point along a straight line in space as a function in time, and then superimposing that graph on the picture of the light moving along its straight-line path.

If the light is moving along the x-axis, you shouldn't be thinking of the sine wave as moving back and forth along the y and z axes. It's telling you what the magnitude of the electrical and magnetic field is at all points in the plane perpendicular to the x axis at any given moment.

bcrowell and DonB
I've heard that nothing can travel faster than the speed of light. Is that actually held to be a scientific truth, and if so what is the basis for that?

The reason I ask, I was watching a video on relativity, and it illustrated a straight-line light beam traveling through space. Superimposed upon the beam was the electromagnetic sine wave that is a part of that light beam. In a way the whole thing looked like a ski boat traveling across a lake, with the skier cutting back and forth across the straight-line path of the boat (wake).

I've skied enough back in the day to know that cutting back and forth across the boat's path makes the skier go at much greater speed than the boat, adding lateral movement to the forward movement. So, I'm wondering that, if the straight-line speed of a light beam is c, then isn't the electromagnetic wave that constantly crisscrosses it going at a speed significantly faster than c?
The short answer: light is nothing like that, and relativity is not a theory of light but of the geometry of spacetime.

If you want to learn about light an easy and entertaining read is Richard Feynman's QED: The Strange Theory of Light and Matter

If the light is moving along the x-axis, you shouldn't be thinking of the sine wave as moving back and forth along the y and z axes. It's telling you what the magnitude of the electrical and magnetic field is at all points in the plane perpendicular to the x axis at any given moment.
Right, I understand that.

Those pictures are misleading, because the lines representing the electrical and magnetic fields aren't really moving back and forth across the path of the light. We're graphing the strength of the electrical and magnetic field at each point along a straight line in space as a function in time, and then superimposing that graph on the picture of the light moving along its straight-line path.
So, you're saying that there is no actual wave from the electrical or magnetic "components" of light? I didn't know that. Maybe this is a different thing altogether, but there is an aspect of light that is a wave -- whatever it is that allows light to pass through a polarized filter when the filter is at one angle, but doesn't allow the same light to pass through when the filter is rotated to a different angle. Is not the total velocity of that oscillating wave not greater than the straight-forward c of the light beam?

Mister T
Gold Member
I've heard that nothing can travel faster than the speed of light. Is that actually held to be a scientific truth, and if so what is the basis for that?
You start by postulating that the speed of light is the same for all observers. It therefore follows that if you were to chase after a beam of light you couldn't make any progress catching up to it, because it would forever recede from you at that same speed. This seems a preposterous idea, and no one would accept it without confirmation.

So there's two categories of confirmations. The first is experiments that directly demonstrate its validity. The second is the seemingly preposterous conclusions that follow from the postulate. Those too have been confirmed overwhelmingly. There is more evidence to support them than there is to support just about any other theory ever created. These ideas were originally met with resistance by the community of scientists, but due to these confirmations they are now, a century later, overwhelmingly accepted.

I've skied enough back in the day to know that cutting back and forth across the boat's path makes the skier go at much greater speed than the boat, adding lateral movement to the forward movement. So, I'm wondering that, if the straight-line speed of a light beam is c, then isn't the electromagnetic wave that constantly crisscrosses it going at a speed significantly faster than c?
In that analogy the water wave is the electromagnetic wave. There's no skier riding it. Evidently it was misrepresented in that video. Some of those videos are done rather well, but others make me cringe when I watch them.

DonB
I've heard that nothing can travel faster than the speed of light. Is that actually held to be a scientific truth, and if so what is the basis for that?
Yes, that is held to be a scientific truth, and the basis for that are experimental results.

It's not like physicists created a theory that predicted a constant speed of light, but rather the other way around: Experiments showed that the speed of light is constant for any observer, and then the physicsts created a theory that can describe these experimental results in a consistent way.

DonB
Nugatory
Mentor
So, you're saying that there is no actual wave from the electrical or magnetic "components" of light? I didn't know that. Maybe this is a different thing altogether, but there is an aspect of light that is a wave -- whatever it is that allows light to pass through a polarized filter when the filter is at one angle, but doesn't allow the same light to pass through when the filter is rotated to a different angle. Is not the total velocity of that oscillating wave not greater than the straight-forward c of the light beam?
It is a wave, you're right about that. But thing that is oscillating is not an object with a position in space, it's the magnitude of the electrical and magnetic fields at each point in space so we can't attach a speed to the back-and-forth waving lines. One way of visualizing what's going on:

The electromagnetic wave is propagating in the direction of the x axis. We position a charged particle somewhere, and we measure the electrical force on it. We find that it experiences a force along the z-axis given by the the time-varying equation ##F_z=A\cos{t}## - the force oscillates between ##A## and ##-A##.

Now we place another particle somewhere else along the x-axis, at a distance ##d## from the first particle. We find that it also experiences a time-varying force along the z-axis, but this force is given by ##F_z=A\cos({t}-d/c)##. That is, the electrical field is at its peak strength at time zero for the first particle and at time ##d/c## for the second particle - it takes time ##d/c## for the peak in the electrical field to move from the first particle to the second, which tells us that the the peak is moving at speed ##c##. I could generalize the equation so that works for any particle anywhere by writing it as ##F_z=\cos(t-x/c)##; we still have the field at any one point oscillating between ##A## and ##-A## and the peaks moving in the x direction with speed ##c##.

We do this with other particles and we find that the forces are the same for all particles in the same plane perpendicular to the x-axis - the y and z positions don't matter, just the x position and the time. That is, no matter where in space you are, the peaks and troughs are moving in the x direction at speed ##c## and there's no sideways anything involved.

You are right that the light is polarized; in this example the electrical field is oriented along the z-axis so that's the direction of polarization. If the electrical field were oriented along the y-axis that would be a different polarization, at right angles.

(Be aware that I've left the frequency of the light out of the equation just to keep things simple, and also that the ##\cos(t-x/c)## formula describes an idealized plane wave. The light waves, flashes, signals, and beams that we see around us are actually fairly complicated combinations - "superpositions" in the lingo - of overlapping plane waves travelling in different directions with different amplitudes and frequencies).

DonB
It is a wave, you're right about that. But thing that is oscillating is not an object with a position in space, it's the magnitude of the electrical and magnetic fields at each point in space so we can't attach a speed to the back-and-forth waving lines. One way of visualizing what's going on:
Thanks. So would it be right to say that the electro/magnetic wave is not so much a separate 'companion' to the light beam (as I've thought), but is rather 'radiated' (in a non-technical sense) from that beam of light?

Mister T
Gold Member
Thanks. So would it be right to say that the electro/magnetic wave is not so much a separate 'companion' to the light beam (as I've thought), but is rather 'radiated' (in a non-technical sense) from that beam of light?
The electromagnetic wave is that beam of light.

Or to put it more precisely, the electromagnetic wave is the model for light.

You start by postulating that the speed of light is the same for all observers. .... This seems a preposterous idea, and no one would accept it without confirmation.

So there's two categories of confirmations. The first is experiments that directly demonstrate its validity.
Thanks. I would be very curious to know what some of those experiments are. One of the main things I would like to get out of my interaction here is to grasp the reality of this concept. So far my search for answers has still left the question unexplained. So, if you could give me a list of some of those experiments that I could look up, I would really appreciate it.

Yes, that is held to be a scientific truth, and the basis for that are experimental results.

It's not like physicists created a theory that predicted a constant speed of light, but rather the other way around: Experiments showed that the speed of light is constant for any observer, and then the physicsts created a theory that can describe these experimental results in a consistent way.
Thanks Smattering. As I just asked someone else, a list of some of those experiments that I could look up and study would be most appreciated.

Nugatory
Mentor
Thanks. So would it be right to say that the electro/magnetic wave is not so much a separate 'companion' to the light beam (as I've thought), but is rather 'radiated' (in a non-technical sense) from that beam of light?
Light IS electromagnetic radiation. I pass electric current through the filament of an incandescent light bulb, the filament heats up, the atoms in the filament bounce around in ways that cause them to radiate electromagnetic waves. That's light, and when it reaches your eyes and triggers the light-sensitive cells in the retina of your eyes (we could just as well have called them "electromagnetic-wave-sensitive cells") you say that the light is shining. These cells also react to different wavelengths and frequencies in different ways, and that is how we sense different colors.

The history here is somewhat relevant. We've known about the existence of light since prehistoric times - it's hard to have functioning eyes and not notice that light exists. Starting in the seventeenth century and continuing well into the nineteenth century, people were observing phenomena such as diffraction, interference, refraction, prisms and spectra that strongly suggested that light was waves of something. Reasonably accurate measurements of the speed of light were made as early as the eighteenth century. So by the nineteenth century, we understood the behavior of light well enough to make really good telescopes, microscopes, eyeglasses, Fresnel lenses, and a had a pretty good sense that light was waves of something - but of what? What was waving?

In 1861 James Maxwell, working in the apparently unrelated field of electricity and magnetism, discovered the fundamental equations that relate electrical fields and charges to magnetic fields. These equations predicted electromagnetic waves... and that these would propagate at a speed that just happened to be equal to the best measured value of the speed of light. Rather than declaring this an amazing coincidence and moving on, Maxwell suggested that the electromagnetic waves his equation predicted were light and that this was the answer to the "what is waving?" question.
It turned out that he was right.

(It also turned out that Maxwell's discovery led to other problems that tormented physicists for the next half-century, until Einstein resolved them in 1905 with the discovery of special relativity. The speed of light as universal speed limit is only one of the many things that followed).

DonB
I've heard that nothing can travel faster than the speed of light. Is that actually held to be a scientific truth, and if so what is the basis for that? ...
The basis for that is the principle of relativity [1,2] and Maxwell equations. A uniform plane electromagnetic wave, which is a fundamental solution to Maxwell equations, propagates at the light speed in all directions. Consequently, when directly applying the relativity principle to Maxwell’s equations, the light speed must be the same in all inertial frames of reference, in other words, the covariance of Maxwell equations requires the constancy of light speed.

[1] A. Einstein, Ann. Phys. (Leipzig) 17, 891 (1905).
[2] A. Einstein, Relativity: The Special and General Theory, Sect. VII (Methuen & Co. Ltd, London, 1920) p. 14.

DonB
The electromagnetic wave is that beam of light.
If that is the case, then doesn't that make the EM wave an actual "thing" (which someone earlier said it is not), and thus in its wave form it is going faster than c?

Mister T
Gold Member
If that is the case, then doesn't that make the EM wave an actual "thing"
Which is why I added this caveat ... "Or to put it more precisely, the electromagnetic wave is the model for light."

(which someone earlier said it is not), and thus in its wave form it is going faster than c?
The wave travels at speed c. Light travels at speed c.

The wave is the model. Light is the thing being modeled. The model of the thing is not the thing itself.

People created the model. People didn't create the thing itself. That's a distinction forming the basis of scientific literacy.

I have no clue how you were led you to the conclusion that the wave goes "faster than c".

DonB
I have no clue how you were led you to the conclusion that the wave goes "faster than c".
Just a jump of logic within my own mind -- can't blame anyone else but me. If the straight-line light beam is going c, then my own logic figured anything traveling along the sine wave superimposed on that beam would have to be going faster. Not saying that is the right way to look at it (apparently), just where it came from.

Mister T
Gold Member
Just a jump of logic within my own mind -- can't blame anyone else but me. If the straight-line light beam is going c, then my own logic figured anything traveling along the sine wave superimposed on that beam would have to be going faster. Not saying that is the right way to look at it (apparently), just where it came from.
Ah... I see. Read Post #7 again. Nugatory's point is that there is nothing riding the crests and troughs of the wave. The only thing waving is fields.

Even in the case of a material wave, like water waves on the surface of a lake, nothing moves along the crests and troughs. Each little parcel of water never travels far from its equilibrium position.

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Nugatory
Mentor
If that is the case, then doesn't that make the EM wave an actual "thing" (which someone earlier said it is not), and thus in its wave form it is going faster than c?
The wave is an actual thing, the same way that a water wave is an actual thing. But the only thing that is moving is the position of the crests and troughs, and they're moving at ##c##. Unlike a water wave, nothing is moving up and down - the electrical field at a each point is just getting stronger until it reaches a maximum, then weaker and falling to zero and growing in the opposite direction until it reaches a maximum in that direction, and then repeating the cycle.

Nugatory
Mentor
Just a jump of logic within my own mind -- can't blame anyone else but me. If the straight-line light beam is going c, then my own logic figured anything traveling along the sine wave superimposed on that beam would have to be going faster. Not saying that is the right way to look at it (apparently), just where it came from.
Nothing is travelling along that sine wave. Its height (distance from a point on the x-axis) is just an easy graphical picture of the strength of the electrical field at that point on x-axis. The field and its strength are real, the sine wave is a graph of its strength.

DonB
After all its simple logic. Everything which existence is directly dependent from EM interactions (electrons, protons and even neutrons do), could not exist if it would travel faster than the very same interactions itself to which it owns its existence in the first place.

The wave is an actual thing, the same way that a water wave is an actual thing. But the only thing that is moving is the position of the crests and troughs, and they're moving at ##c##. Unlike a water wave, nothing is moving up and down - the electrical field at a each point is just getting stronger until it reaches a maximum, then weaker and falling to zero and growing in the opposite direction until it reaches a maximum in that direction, and then repeating the cycle.
So, there really is a wave, but it is not so much matter in itself as it is a measure of the fluctuation/oscillation of the electrical field. So, the travel of the light beam graphed along the X axis is a measure of distance, but the oscillation of the electrical field (plotted as plus and minus in the Y direction) is not a measure of distance, but of charge. Right? Thus to graph the wave as riding upon the beam does not actually imply all that one might infer from it -- namely, there is no valid comparison of the distance plotted along the X axis (i.e., the distance the light travels) to the distance plotted along the Y axis (the measure of the charge fluctuation in the electrical field). To compare the two is to compare apples to oranges -- right?

Nugatory
Mentor
-- right?
Right

DonB
Right
That explains at least a part of my overall misunderstanding, for I somehow assumed both X and Y to be representing the same units of measure. And whether there was something that actually 'rode' that wave, or even if the wave was a fluctuation/oscillation, as the sine waves nears the X axis the movement/fluctuation in the Y direction was greater than in the X. And since X represented the speed of light, the Y-component movement/fluctuation would have thus been exceeding c -- which prompted my question.