why does light have a finite speed

The book is called: Physics for Scientists and Engineers its written by Serway and Jewett. It is pretty dense for a general physics textbook but only covers topics upto and including relativity. Chapter 16 is just refering to wave mechanics.

I am still not sure it is implied in the equations themselves that electric fields induced in free space are then inducing magnetic fields and so on with a delay. These equations were determined from experiments looking at electricity and magnetism which were properties of some material object like a conductor. Take Faraday's Law for example: A changing magnetic flux is inducing an emf in space, and because the emf is equal to the line integral of E*ds there is an E field induced also. That electric field is said to exist even if there is no conductor loop or charged particle there to detect it. But once you put the loop or charged object in the changing field the emf can be seen. The point is: we know a conductor loop in a potential difference will have a current set up in it and so will create a magnetic field. But we do not really know if alternating magnetic fields within empty space with nothing around them can create electric fields that are then in turn capable of creating magnetic fields. Or what kind of delay that might have.

It seems more likely to me that if you have a antenna like a hertzian dipole antenna(Just a long straight antenna with oscillating current), that electric fields due to the oscillation of the current are simply propagated away, oscillation by oscillation, from the source out into space at the speed of light. And along with them the magnetic fields too. Especially since the decrease in the strength of the electromagnetic wave will be proportional to 1/r just as you would expect from a steady current or a static charge distribution along a long linear conductor. I do not want to imagine how difficult it would be to calculate the decrease in field strength of E fields setup by B fields and so on in space.

I'm not sure all that is true. In the first place the now quaint metaphor of the "solar wind" is an expression of the momentum of photons (recall that in gas dynamics pressure is the averahge momentum of the gas molecules.).Lagrangian mechanics alsu employs the six coordinates of phase spoace, three of which are the momentum of the body in question.

I'm not denying that electromagnetic radiation has momentum. But the question was whether this momentum requires mass --- and it doesn't. Electromagnetic radiation can have momentum without having mass. And as I said earlier, Lagrangian and Hamiltonian have no problem with that.

You're right about the math, but I have a problem with the association of momentum with wave energy. No mass = no momentum.

For a brief summary:
Take the equations for energy and momentum
E= (mc^2)/[√{(1−v^2)/c^2}]
p= (mv)/[√{(1−v^2)/c^2}]

Solving them algebraically, and eliminating v gives you
E = (mc^2)^2 + (pc)^2

What you should be thinking is No movement = No momentum, and not No mass = No momentum.
This can be seen as follows:
E = (mc^2)^2 + (pc)^2
When there is no movement, then there is no momentum (p = 0) and the equation becomes E = (mc)^2.
However, if the particle in question is mass-less, light for example, then m=0, and E = pc, which means that the energy of a mass-less particle like light is the same as the momentum to the factor of light. More importantly, the closer the energy of something is to (p*c) the closer that something behaves like light.
We can rewrite that equation for v.
v = c*[(pc)/E]
As momentum increases, (pc) becomes closer and closer to equaling the E (energy) so the ratio gets closer to one (0.9999...->1) and thus speed gets closer and closer to the speed of light. Light, w/ no mass, is when pc = E.

I agree the notion is counterintuitive. But when has counterintuitiveness ever stopped a physical theory? Radiation pressure was discovered before Planck's quantum hypothesis. Theorists explained it at the time within the classical framework laid out in Maxwell's equations. This was possible because classical mechanics had already been re-framed in terms where momentum is a derivative of energy over space, independent of mass. Physical theory therefore had no problem with the notion that light transmits has momentum and, when reflected, transmits it to the body reflecting it. I wouldn't be surprised, though, if physical theorists had had as much of a problem with the notion as you do. After all, it is counterintuitive.

Thanks That was good !

I'm aware of the dual nature of light (and other like radiation), but did not grasp the point you made by expressing the energy in terms of relativistic momentum.

There I've fixed some mistakes. Sorry that was the nerd in me acting up

Good summary by the way, I like it.

Oh wow, thanks for catching those mistakes. Wrote that right before leaving home for work, so was in a bit of a hurry.

Let me first say that based on the level of the content of some of your other topics I don’t see you as the person described in the initial post on this topic.
So, if you don’t already know this stuff, here are some things you might consider.


What I think you should focus on is the DEFINES. One might say that is the essence of all science. The answer is yes there is an answer to everything. The answer is: it depends on how you look at it, i.e. how you choose to define things. You also need to get used to metaphysical incertitude.

Let’s start with something easy and tangible: The height of an object in geosynchronous orbit (what height is a satellite at if it is always over the same point on the Earth). Yet if you look this up you could well find that authoritative sources provide (slightly) different answers; which is “right” -- probably all, as the difference is probably based on using differing coordinate systems, or slightly different values for the Earth's mass-center position.

A more abstract example is the question what is the radius of the hydrogen atom? Would it surprise you to know that the answer is: 5 × 10-11 meters (that is one half angstrom)?

Would it surprise you to learn that the radius of the hydrogen atom is: 4 × 10-13 meters?

Would it surprise you to learn that the radius of the hydrogen atom is: 3 × 10-15 meters?

If you are not easily surprised, would learning that each answer above is correct surprise you?

Well they are all true.

Bohr radius = 5 × 10-11 meters
Compton wavelength = 4 × 10-13 meters
Classical electron radius = 3 × 10-15 meters

The differences originate in the differing “givens” used.

A third example is provided in the question of the “absolute” mass of the proton. Even leaving aside that there are a number of masses for the proton: rest mass, relativistic mass, invariant mass, etc.; what answer do you get if you just measure the mass of the darn thing!!!

Would it surprise you to know that the mass changes depending on how “close” you choose to look?

The “closer” you look the more massive it becomes. To complicate this Disneyland ride even more the rate of increase is not linear, it is in fact, an example of a Fractal.

Would it surprise you to find it was suddenly “Disneyworld on acid” in that the closer you looked and the shorter time you took to look the more likely the chance that you would not be looking at a proton but a neutron or a neutral pion, or any number of particles other than a proton? Yet when you look again the proton is sitting there waiting for you?

Would it surprise you to know that if you look too closely at the proton rather than a mass measurement you would have destroyed the proton and replaced it with two energy particles such as mesons?

Whether or not any of this surprises you, does it give you any new insight into the nature of the questions you are asking, if not the answwers to the specific questions themselves?

Would it surprise you to find out that I just made all that up, or surprise you more to find out that I didn’t.

Only the Bohr radius is the actual radius of the hydrogen atom. The compton wavelength has nothing to do with hydrogen atoms. And the classical electron radius is greater than the proton radius which is 1833 times heavier. The electron probably does not have a radius.

Yes you are right. As if that wasn’t obvious too you, right. I was trying to make the point of the Compton wavelength and classical wavelength of the electron. For what it is worth (if you are wondering, for example, how the hydrogen radius got in there); I was also working on an answer to a question on length scales I got from my friend’s son (away at school) and apparently got caught between two ideas. It was too late for the edit button after I read the post.

Thanks for the fix. Mia culpa to all. Like this one, my mistakes are often impressive. I should take my responses more seriously and proof read. I am afraid to look at what I just emailed Shawn.

Hey if its any consolation I had to look up the compton wavelength I was getting it confused with de Brolie's wavelength. There is a lot of physics out there to get mixed up on.