Why does light travel at the speed it does?

[JDługosz]

I don't know, I think that dodges the question. What we want to know is why a fly can have variable speeds but light's speed is fixed.

Speculation: the problem is that we think of space and time as independent dimensions, but they're not. 'spacetime'' is a coupled 2d system (parameterizing 3d space as 1 curvey dimension).

Try:
http://arxiv.org/abs/physics/0302045"

It follows from the general principles of reciprocity and symmetries, and it must be so.

 

[jonathanplumb]

I'm just hypothesizing here, but consider this:

Ask yourself: why does a bullet travel at the speed it does out of a gun? Granted there's lots of velocities a bullet can exit a muzzle at, if all of the shots were performed in a vacuum with the exact same amount of gunpowder (regardless of the shape or size of the bullet), all of the bullets would travel at exactly the same speed. This is because no outside forces are acting on the bullets, and all of them are projected with the exact same force.

First let's look at how light is formed. Light photons are formed when energy is applied to an atom. The energy excites the electrons pushing them away from the center of the atom until they cannot get any further away from the atom and they release that massive energy buildup in the form of a photon, then they sink back down close to the atom to repeat the process. The photon travels outward in all directions, kind of like a field (stupid theories of rays...).

Now think of the light in comparison to a bullet. With light, you have energy being applied (like the primer of the bullet firing off and igniting the gunpowder). As the energy builds up, the electrons are forced to the outside until they can no longer contain the energy (like the gunpowder building up pressure before the bullet actually fires out of the casing). Finally the energy explodes out and a photon is released (like the bullet firing from the barrel).

The photon travels at exactly the speed dictated by the amount of energy required to release the photon. The speed of light changes very little outside of a vacuum because very few forces have the ability to act on the photon (much like when we fired the bullets in the vacuum).

That is why a photon travels at the speed it does. It's a representation of the actual amount of raw energy released as photons.

I have, however, had a hypothesis for a long time that light of different amplitudes and wavelengths actually travel at different speeds, but the difference is hardly measurable with our current systems of measurement.

 

[Dead Boss]

That's totally wrong. Photons travel with speed c regardless of how they are created. Different photons have different energies, and they still travel the same speed.
Also your hypothesis is wrong.

 

[furqi24]

hi 2 all...
it is quantum theory of light...light travel 8 very high speed...

 

[Dale]

My intuition is throwing up some red flags, so I'd want to dig deeper before I'm comfortable, but I appreciate your response. ...
Good point, and this is actually one of a few things that bothers my intuition, but I'll get to grips with it.

No problem, my intuition also gave some red flags:
https://www.physicsforums.com/showpost.php?p=2020276&postcount=93

Yes, I would like to see those calculations, thank you.

I have attached the notebook. It may be hard to read, but basically I am contemplating some sort of "universe change" which really alters c, G, h, or vacuum permittivity (the primed variables are post-change and the unprimed are pre-change) and then seeing how measurements change afterwards.

 

[stevenb]

No problem, my intuition also gave some red flags:
https://www.physicsforums.com/showpost.php?p=2020276&postcount=93


I have attached the notebook. It may be hard to read, but basically I am contemplating some sort of "universe change" which really alters c, G, h, or vacuum permittivity (the primed variables are post-change and the unprimed are pre-change) and then seeing how measurements change afterwards.

Thank you very much. This does look interesting, and I'll need some time to think deeply on this.

Just looking superficially, I'm intrigued by the fact that the measurement of speed seems unaffected provided that the product of fine structure constant and the gravitational coupling constant does not change. More specifically, speed measurement seems to scale inversely with the square root of the product of these dimensionless constants.

Based on this, would you say that this allows you to say to the OP that asking "why does light travel at the speed it does?" is equivalent to asking "why does the product of two dimensionless constants (which could be viewed as one effective dimensionless constant) have the value it does?"

In particular, why does {{1}\over{\sqrt{\alpha \; \alpha_G}}}\approx 2.8 \times 10^{23} ?

 

[JDługosz]

Based on this, would you say that this allows you to say to the OP that asking "why does light travel at the speed it does?" is equivalent to asking "why does the product of two dimensionless constants (which could be viewed as one effective dimensionless constant) have the value it does?"

My feeling is that c is only meaningful when related to different things. His explanation of comparing different physical phenomena, e.g. a meter stick is some number of atoms strung together in a rod vs. the distance traveled in a specified time interval, makes that more explicit. Since you also need different ways of measuring time, e.g. a pendulum vs. an atomic clock, you are relating gravity, electromagnetism, and the structure of space-time.

If you throw in more such measurements, you will need more constants: one for each fundamental force, perhaps. In fact, I might suppose that this kind of thing determines just what is considered a separate "free" constant in physics in the first place. If you change everything needed, in sync, so that all the dimensionless constants stayed the same, then all you did was re-scale everything.

The only thing we can ever measure is the relationship between things, not one thing itself. So only the overall pattern of relationships matters.

 

[stevenb]

My feeling is that c is only meaningful when related to different things. His explanation of comparing different physical phenomena, e.g. a meter stick is some number of atoms strung together in a rod vs. the distance traveled in a specified time interval, makes that more explicit. Since you also need different ways of measuring time, e.g. a pendulum vs. an atomic clock, you are relating gravity, electromagnetism, and the structure of space-time.

If you throw in more such measurements, you will need more constants: one for each fundamental force, perhaps. In fact, I might suppose that this kind of thing determines just what is considered a separate "free" constant in physics in the first place. If you change everything needed, in sync, so that all the dimensionless constants stayed the same, then all you did was re-scale everything.

The only thing we can ever measure is the relationship between things, not one thing itself. So only the overall pattern of relationships matters.

Yes, I'm starting to get it. The idea of comparing is the key point. It's also important to know exactly what is being compared, as highlighted by the following.

It occurs to me that the new definition of the meter is based on the speed of light. A meter is now the distance light travels in 1/299 792 458 seconds. This is significantly different than the earlier definitions based on a standard rod. The old definition is comparable to the above discussion about using Bohr radii as a ruler, while the new definition uses light itself and a timer. The interesting thing is that the new definition will always give us the same numerical value for c, irrespective of the values of dimensionless constants. Even if the speed of light were somehow changed in a meaningful physical way, the number we get from the definition would not change, since the number is built into the definition. But, it's important to distinguish between a real physical change and a numerical change. The new definition is always the same number, but a real change can still be a function of (fictitious) changes in dimensionless constants.

 

[JDługosz]

Even if the speed of light were somehow changed in a meaningful physical way, the number we get from the definition would not change, since the number is built into the definition.

Defining the meter in terms of c is still bringing in other parts of the universe in your definition. In particular, what is a "second"? So the definition a particular known distance in the time dimension with its terms in the space dimension. "This much time is eqv. to this much space" is fundamental, and you can choose some amount of each to call your measurement units.

So how do you know what the "second" is? Defining it with the specific frequency of light from a specified energy level transitions, it relates to the energy level of that atom; that is, the behavior of the electron on the quantum level. The mass of the electron, Planck's constant, the charge of electrons, and the force associated with units of that charge, all have to do with it. The dimensionless constant associated with all that is what's called the "fine structure constant".

Now we keep pointing out that c is not a dimensionless constant. But the idea that space-time "just is", I don't know what that is properly called. But when we measure c, we are really measuring properties of the electron's behavior. That is, we are labeling other behaviors based on our chosen units in space and time. That's the opposite way around of what you think you are measuring.

Everything is connected together. You start out by picking something and calling it a unit. Then everything else is measured relative to that. Consider a drawing of a complex shape, with any line between any two features measured. You can't just change one of those lines' lengths: if you move the point, all the other lines change too. If you propagate changes to preserve the same measurements, you find that you just rescaled the whole drawing.

 

[pallidin]

c is extremely slow with respect to the totality of our universe considerations.
For example, traveling at c can take thousands, perhaps billions of years to reach some galaxies.
Wholly unsuitable for many practical purposes. Astronomical "observation" beyond our solar system is much in the past. Even viewing our own sun is a 9 minute delay.

Why is c, c? Not sure, but it's a constant. Is it "immutable" ?
Unknown, but I hope it is not, as it is VERY slow.

 

[diazona]

Why is c, c? Not sure, but it's a constant. Is it "immutable" ?
Unknown, but I hope it is not, as it is VERY slow.

Unless relativity is pretty drastically wrong, c is an invariant constant. But it doesn't necessarily have to be the limit on how fast you get from point A to point B (if wacky things like stable wormholes are possible, that is).

 

[stevenb]

Defining the meter in terms of c is still bringing in other parts of the universe in your definition.

It's not "my" definition, it is "the" definition, and yes it does bring other parts of the universe. I wasn't implying otherwise. I was only pointing out that the new definition of the meter forces a fixed number to be assigned to the value of c in meters/second. So the number used to describe c in m/s itself does not relate physically to any of the parts of the universe and no physical change would change the number. You could redefine the second to be an hour and the number we get for c in m/s would be exactly the same. No matter how you change the fine structure constant (if you could change it) it would not change the number used to describe c, using the new definition of the meter. However, a change in the fine structure constant would drive real physical changes in the speed of light, even though the number would not change.

Interesting story about this definition change. Back in 1985, my physics teacher for optics assigned the class the question of looking up the definition of the meter. He was shocked to find that he had to learn from a dozen or so students that the definition of the meter had been recently changed. It was a little embarrassing for him, but he was a good sport about it, since he could have easily hid the fact that he did not know.

 

[brainstorm]

I don't know, I think that dodges the question. What we want to know is why a fly can have variable speeds but light's speed is fixed.

How can something without mass/inertia accelerate or decelerate? If it has energy, so it can't stay still, right? But if it has no mass, any amount of force would propel it to infinite velocity, right? Another way to put that would be that for a given amount of force, acceleration approaches infinity as mass approaches zero, right? But can acceleration = infinity without infinite energy, even for massless particles/waves? I'm thinking that it is logical that a given amount of radiation has a defined quantity of energy and therefore cannot travel beyond a certain velocity. That is also logical if energy is the same as momentum, because momentum approaches infinity as mass approaches zero, but radiation doesn't transfer infinite momentum between its source and destination.

This is all logical to me, but I'm really just reasoning this from these other definitions. I hope this isn't considered speculation, because I'm not speculating - just interpreting the other definitions in light of the issue of why the speed of radiation would be limited from a logical perspective.

 

[diazona]

Well, but if you think about it that way (i.e. light has energy and that's why it can't exceed a certain speed), it makes sense that the maximum speed of light would depend on how much energy it has. And experimental observations show pretty conclusively that that's not the case.

Also, where did you get that momentum approaches infinity as mass approaches zero? That's certainly not the case in reality - if anything, momentum is proportional to mass. p=γmv for massive particles. (Not for photons)

 

[Dale]

Just looking superficially, I'm intrigued by the fact that the measurement of speed seems unaffected provided that the product of fine structure constant and the gravitational coupling constant does not change. More specifically, speed measurement seems to scale inversely with the square root of the product of these dimensionless constants.

Based on this, would you say that this allows you to say to the OP that asking "why does light travel at the speed it does?" is equivalent to asking "why does the product of two dimensionless constants (which could be viewed as one effective dimensionless constant) have the value it does?"

In particular, why does {{1}\over{\sqrt{\alpha \; \alpha_G}}}\approx 2.8 \times 10^{23} ?

Yes, but I think it is necessary to be a little more specific. This is the speed of light as measured by pendulum clocks and rods. The gravitational coupling constant enters in because I deliberately chose a pendulum clock for the measurement of time. If you used an ectromagnetic means to measure time then you would only have the fine structure constant.

 

[stevenb]

Yes, but I think it is necessary to be a little more specific. This is the speed of light as measured by pendulum clocks and rods. The gravitational coupling constant enters in because I deliberately chose a pendulum clock for the measurement of time. If you used an ectromagnetic means to measure time then you would only have the fine structure constant.

Ah, yes, again it gets back to being careful about comparisons. Thank you! Simple and yet mind boggling at the same time.

 

[MarsWTF]

because speed of light is max possible speed in the universe. and photons, to carry some energy, must to use this speed as their mass is 0.
So if mass=0 to carry some energy we must have speed=~endless

itsa like V and A in the electricity, if A is low V must be high to carry some real power

 

[brainstorm]

Well, but if you think about it that way (i.e. light has energy and that's why it can't exceed a certain speed), it makes sense that the maximum speed of light would depend on how much energy it has. And experimental observations show pretty conclusively that that's not the case.

If the amount of energy in radiation determined its speed, what would govern its frequency/wavelength? Then you would expect all radiation to have the same wavelength but travel at different speeds relative to its energy, wouldn't you?

Furthermore, isn't it possible to say that red-shifted light has actually sped up relative to spacetime? After all, what would you have to measure its speed against except a similar beam of radiation that wasn't shifting? Yet if different frequencies of radiation traveled at different speeds, you would expect images to get fragmented according to frequency over long distances, which means that all frequencies must travel at the same speed, right?

Also, where did you get that momentum approaches infinity as mass approaches zero? That's certainly not the case in reality - if anything, momentum is proportional to mass. p=γmv for massive particles. (Not for photons)

I may have said that wrong. I meant the same thing as with the f=ma relationship. A specified amount of momentum would result in velocity approaching infinity as mass approaches zero, right? Doesn't it make sense for the amount of momentum transmitted by radiation to be variable, velocity would be constant and "mass" would have to vary according to the amount of energy transmitted? If velocity varied with momentum, then you would end up back with the problem of wavelength variation - i.e. why would some of the energy get expressed as velocity and the rest as frequency/wavelength? Plus, how would the radiation change velocity without mass/inertia? If it has no mass/inertia, it has to always be moving at maximum velocity, right?

 

[MarsWTF]

they assumed that there was an all-pervading substance (they called it “ether”) that “carried” light waves

Now its called "dark matter"

 

[novop]

They're actually completely unrelated.

 

[diazona]

If the amount of energy in radiation determined its speed, what would govern its frequency/wavelength? Then you would expect all radiation to have the same wavelength but travel at different speeds relative to its energy, wouldn't you?

Well, in reality, frequency is related to energy by f=E/h (h = Planck's constant), and wavelength is related to frequency by λ = c/f. Those relations would still make sense, even if the speed of light varied by its energy (i.e. if c were a function of f). It wouldn't necessarily be the case that all radiation would have the same wavelength; that would only be true if the speed were linearly proportional to the frequency.

Come to think of it, this is exactly what happens when light travels through matter. Its speed drops by a factor (the index of refraction) which depends on the frequency. This is how a prism is able to work.

Furthermore, isn't it possible to say that red-shifted light has actually sped up relative to spacetime? After all, what would you have to measure its speed against except a similar beam of radiation that wasn't shifting? Yet if different frequencies of radiation traveled at different speeds, you would expect images to get fragmented according to frequency over long distances, which means that all frequencies must travel at the same speed, right?

Yeah, that's exactly the sort of experimental evidence I referred to. Measurements of light pulses from distant supernovae and the like show that different frequencies of radiation all arrive at essentially the same time. As far as the thing about red-shifted light, I don't really understand your argument. Red-shifted light has lost energy, but it still travels at the same speed. You could measure that with a ruler and stopwatch (or, more likely, interferometer).

I may have said that wrong. I meant the same thing as with the f=ma relationship. A specified amount of momentum would result in velocity approaching infinity as mass approaches zero, right?

According to the classical relationship p=mv, then yes. But that isn't exactly accurate. Special relativity tells us that the correct formula (for massive particles) is
p = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}}
As the mass approaches zero, the factor v/√(1-v²/c²) approaches infinity, but v itself approaches the speed of light, c.

Doesn't it make sense for the amount of momentum transmitted by radiation to be variable, velocity would be constant and "mass" would have to vary according to the amount of energy transmitted?

Yep, exactly. The momentum of a photon is given by p = E/c, where E is the energy. Back in the day (1930's, 40's, 50's), people used to define this thing called "relativistic mass" which was the amount of mass that, at rest, would have a given amount of energy - in other words, m_rel = E/c^2. Using that concept, you could write the momentum of a photon as p = m_relc, and the momentum of a massive particle (which I mentioned above) as p = m_relv. But eventually the concept of relativistic mass turned out to be really confusing, and most physicists abandoned it.

If velocity varied with momentum, then you would end up back with the problem of wavelength variation - i.e. why would some of the energy get expressed as velocity and the rest as frequency/wavelength? Plus, how would the radiation change velocity without mass/inertia? If it has no mass/inertia, it has to always be moving at maximum velocity, right?

Right. At least, it is true that massless particles always move at the maximum possible velocity, c (in a vacuum, at least), and you've got a decent intuitive argument why that should be the case.

 

[brainstorm]

It wouldn't necessarily be the case that all radiation would have the same wavelength; that would only be true if the speed were linearly proportional to the frequency.

This is a somewhat ridiculous hypothetical discussion, but if both speed and frequency of EM waves varied according to their energy, what would determine how much energy went into speed and how much went into frequency? That's why I say it makes more sense that the speed is fixed and frequency is variable, since it can't accelerate and decelerate without mass/inertia.

Come to think of it, this is exactly what happens when light travels through matter. Its speed drops by a factor (the index of refraction) which depends on the frequency. This is how a prism is able to work.

But this is due to variability in the speed of absorption and re-emission within the substance, right? The waves themselves don't slow down between the particles, right? Some just take longer to get absorbed and re-emitted per-particle. Would that have to do with the acceleration/deceleration rate of electrons?

As far as the thing about red-shifted light, I don't really understand your argument. Red-shifted light has lost energy, but it still travels at the same speed. You could measure that with a ruler and stopwatch (or, more likely, interferometer).

What I was trying to say was that the number of waves per unit length of the beam decreases with red-shift, but you could also say that the waves slowed down because there's nothing to measure them against except themselves or other EM waves from the same source, which have all red-shifted (or slowed down) together, no? This sounds like "tired light," which I've heard has been disproven, but I can't remember how - if it was even explained in the first place.

As the mass approaches zero, the factor v/√(1-v²/c²) approaches infinity, but v itself approaches the speed of light, c.

But the reason the speed of light itself would be fixed (topic of the OP) would be because its momentum is fixed, right? It doesn't make sense that something could traverse infinite distance instantaneously without infinite energy, would it?

Right. At least, it is true that massless particles always move at the maximum possible velocity, c (in a vacuum, at least), and you've got a decent intuitive argument why that should be the case.

Thanks. Your history lesson was also intuitively helpful for understanding how physics has evolved in terms of comparing/equating mass and energy.

 

[diazona]

This is a somewhat ridiculous hypothetical discussion, but if both speed and frequency of EM waves varied according to their energy, what would determine how much energy went into speed and how much went into frequency? That's why I say it makes more sense that the speed is fixed and frequency is variable, since it can't accelerate and decelerate without mass/inertia.

It wouldn't necessarily have to be the case that part of the energy goes into speed and part goes into frequency. For example, in quantum mechanics, a particle has a speed and a frequency (more precisely: its associated wavefunction has a frequency), both variable, but there's no split of the energy between the two. And even if the energy were split between frequency and speed in that way, there's nothing general you could say about how exactly it would be split; it would depend on the model. I definitely do agree that it makes more sense to have the speed fixed.

But this is due to variability in the speed of absorption and re-emission within the substance, right? The waves themselves don't slow down between the particles, right? Some just take longer to get absorbed and re-emitted per-particle. Would that have to do with the acceleration/deceleration rate of electrons?

(1) Yes, (2) right, and (3) I don't think so. Absorption and reemission generally have to do with the electrons changing energy levels within their atoms and molecules, which is a purely quantum process, and acceleration is not really a useful (or well-defined) notion in quantum mechanics.

What I was trying to say was that the number of waves per unit length of the beam decreases with red-shift, but you could also say that the waves slowed down because there's nothing to measure them against except themselves or other EM waves from the same source, which have all red-shifted (or slowed down) together, no?

No... what I was saying before is that you could actually use a physical device which measures the speed of light, like an interferometer. That would give you something to measure the waves against, separate from any other waves that might be around.

This sounds like "tired light," which I've heard has been disproven, but I can't remember how - if it was even explained in the first place.

Wikipedia seems to have some good information: http://en.wikipedia.org/wiki/Tired_light

But the reason the speed of light itself would be fixed (topic of the OP) would be because its momentum is fixed, right?

No, light does not have fixed momentum. You can (theoretically) make a light ray with any amount of momentum. For light (and massless particles in general), the amount of momentum it has is completely unrelated to its speed.

It doesn't make sense that something could traverse infinite distance instantaneously without infinite energy, would it?

No it doesn't, but nothing does this...

Glad I could help out with the info about relativistic mass, by the way

 

[Acut]

@OP: If I'm not mistaken, all waves that don't need material medium to propagate will travel at the speed of light. Besides light, gravitational waves travel at c.

I think I saw a very elegant proof of this in one of Landau's books.

 

[brainstorm]

No, light does not have fixed momentum. You can (theoretically) make a light ray with any amount of momentum. For light (and massless particles in general), the amount of momentum it has is completely unrelated to its speed.

That's not what I mean. I mean that radiation-emission can be described as a certain amount of kinetic energy momentum being converted into radiation. So, for light to move at unlimited speed it would have to gain energy that was not imparted in it during its initial creation/emission. The OP asked why light's speed is limited.

Further, I would guess that light's speed-limit is due to the relationship between the amount of momentum/energy that can be converted into EM radiation by an electron and the distance that the electron moves when generating the radiation. The reason I suspect this is because I don't see how an electron could generate a wavelength shorter or longer than the distance it moves in creating the wave. Likewise, if that particular wave traveled at a faster or slower speed than C, wouldn't it propagate more or less energy than it was endowed with to start with, which would violate conservation of energy?

Actually, this implies that an electron would have to move very far to generate lower frequency waves, which doesn't really make sense, does it? How CAN an electron generate a radio wave? Does it have to do with the speed of electron motion vis-a-vis the universal propagation speed of massless radiation?

 

[diazona]

Oh, OK, sorry for misinterpreting you. I guess you meant that the momentum of a light ray is constant over time, which is true as long as it doesn't interact with anything (not even gravity).

The thing is, if you even admit the possibility that light could move at infinite speed, why wouldn't it move at infinite speed from the moment of its emission? That's the only way I could see a theory with an infinite speed of light making sense. Even if the light could somehow gain energy en route, it makes sense that a finite amount of energy would only increase its speed by a finite amount. So if the light was initially emitted with an amount of energy such that it moved at finite speed, there would be no way for it to ever move at an infinite speed except by imparting an infinite amount of energy.

As far as EM wave generation is concerned, what really matters is how fast the electron moves, not how far it moves. Actually, not even that - what really matters is how much it accelerates. We usually think of electrons moving up and down in sine waves to generate EM radiation, and if you have an electron oscillating really slowly, it would create a very low-frequency (long-wavelength) wave even without moving very far. The distance the electron moves has basically nothing to do with the resulting wave.

Honestly, I don't understand what you're saying about the speed limit being due to the relationship between momentum/energy and distance.

 

[brainstorm]

Interesting exchange we're having. It's particularly appealing to me that I haven't been called an idiot yet, either implicitly or explicitly.

Oh, OK, sorry for misinterpreting you. I guess you meant that the momentum of a light ray is constant over time, which is true as long as it doesn't interact with anything (not even gravity).

Because it would expend some of its energy in the interaction?

The thing is, if you even admit the possibility that light could move at infinite speed, why wouldn't it move at infinite speed from the moment of its emission?

As I've said, I can't think of any way something without inertia could change speeds. Any amount of momentum would always result in maximum velocity without momentum, as far as I can reason.

So if the light was initially emitted with an amount of energy such that it moved at finite speed, there would be no way for it to ever move at an infinite speed except by imparting an infinite amount of energy.

So this explains why its speed is limited and not infinite. But what determines the limit, then, as the OP asks?

As far as EM wave generation is concerned, what really matters is how fast the electron moves, not how far it moves. Actually, not even that - what really matters is how much it accelerates.

So the mass of the electron multiplied by its acceleration is the amount of force it sends out as radiant energy? So, for example, a black body particle heating up accelerates its electrons with a certain amount of force/energy and that causes the frequency of the light emitted? What determined how much of that energy gets conducted or convected to other particles and how much is emitted as radiation, then?

We usually think of electrons moving up and down in sine waves to generate EM radiation, and if you have an electron oscillating really slowly, it would create a very low-frequency (long-wavelength) wave even without moving very far. The distance the electron moves has basically nothing to do with the resulting wave.

What do you mean exactly by oscillating? Are you referring to an atomic electron? free electron? In what situation does it oscillate? My understanding was the electron changes orbital levels and releases energy as it drops back into a lower energy orbit. Can it continuously rise and fall in its orbit, continuously variable in frequency?

Honestly, I don't understand what you're saying about the speed limit being due to the relationship between momentum/energy and distance.

I don't know the exact specs for this, but let's say 1km of red light carries 1million waves (I'm sure it would be exponentially more, but this is just to illustrate what I'm saying). If the light moved faster, the 1 million waves would arrive within a shorter period of time and with more intensity, right? So for a given amount of energy to be expressed as a particular wavelength of light, wouldn't the speed of the waves have to be such that the correct amount of energy was delivered in the amount of time it took the waves to be emitted?

Where I get stuck is what the relationship is between the inertia of an electron and the distance between the electron and nucleus. It seems like this would be the key to establishing a relationship between the speed of light and distance as we measure it according to material volume.

 

[diazona]

Interesting exchange we're having. It's particularly appealing to me that I haven't been called an idiot yet, either implicitly or explicitly.

Oh wait, did I forget to do that? nah, just kidding. I've seen a few idiotic discussions on these forums and this isn't one of them.

And thank you in turn for your intelligent responses

Because it would expend some of its energy in the interaction?

Yep, exactly. Or it could gain energy from the interaction.

As I've said, I can't think of any way something without inertia could change speeds. Any amount of momentum would always result in maximum velocity without momentum, as far as I can reason.

I definitely agree that something without inertia shouldn't sensibly be able to change its speed. But regarding the second sentence, remember that for massless particles, momentum is completely independent of velocity. Having any certain amount of momentum doesn't tell you anything about the velocity. Although, I suppose your reasoning is fine as an intuitive argument. If it helps you make sense of the fact that photons always travel at speed c, by all means go ahead and use that as a memory aid to yourself.

So this explains why its speed is limited and not infinite. But what determines the limit, then, as the OP asks?

That is the fundamental question, isn't it... I don't think physics has an answer for that. I mean, if you want to know why it's 299792458 m/s, that's because of the way our particular units (the meter and the second) are defined: people chose a random distance to call the "meter" and a random time interval to call the "second", and it just turned out that the speed of light was 299792458 m/s. (Originally that was only approximate, then the meter was redefined to make that number exact)

But asking why, on a more fundamental level (independent of human units) the speed of light has the value it does is not a trivial question. Personally I would even say it's kind of meaningless, because the laws of physics themselves only seem to select one "natural" system of units, the Planck units, and in those units the speed of light is necessarily 1. But I guess that's getting into speculation - it's just my opinion, and as far as I know there's no consensus on this. (Most people probably don't even think about it)

So the mass of the electron multiplied by its acceleration is the amount of force it sends out as radiant energy?

Be careful there, force and energy are different quantities. The mass of the electron multiplied by its acceleration is the force exerted by whatever is making the electron move, but that's not necessarily related to the amount of EM energy it radiates. In order to calculate the energy, you need a different formula, the Larmor formula:
P = \frac{e^2a^2}{6\pi\epsilon_0 c^3}

So, for example, a black body particle heating up accelerates its electrons with a certain amount of force/energy and that causes the frequency of the light emitted? What determined how much of that energy gets conducted or convected to other particles and how much is emitted as radiation, then?

Blackbody radiation is actually something a little more complicated, because it's a statistical phenomenon. It arises from the average behavior of large numbers of particles interacting with each other. The individual photons emitted from a blackbody generally come from collisions between particles (not atomic energy level transitions), but if you were to look at the individual collisions, they'd seem pretty random. It's only when you put a large number of them together that you see a pattern in the frequencies.

For a blackbody, it's the temperature that determines how much energy is radiated and how much isn't, but that's only when it's in equilibrium. In general, a blackbody starts out either emitting more radiation than it absorbs or absorbing more than it emits, but in either case, over time, the emission rate and absorption rate will get closer together as the blackbody's temperature approaches that of its surroundings. (Unless it has some internal energy source, like a star) Again, this is all a large-scale statistical phenomenon. If you looked at the energy transfer between individual particles, it'd look pretty random, although it would be subject to the laws of kinematics (or rather, quantum scattering theory, I guess).

What do you mean exactly by oscillating? Are you referring to an atomic electron? free electron? In what situation does it oscillate? My understanding was the electron changes orbital levels and releases energy as it drops back into a lower energy orbit. Can it continuously rise and fall in its orbit, continuously variable in frequency?

No, you're right, atomic electrons do only undergo discrete jumps between energy levels. What I was talking about with the oscillations was a free electron, e.g. in an antenna, that is being pushed back and forth along a straight line (the antenna) in a sinusoidal motion.

I don't know the exact specs for this, but let's say 1km of red light carries 1million waves (I'm sure it would be exponentially more, but this is just to illustrate what I'm saying). If the light moved faster, the 1 million waves would arrive within a shorter period of time and with more intensity, right?

Well... that depends on what happens when the light speeds up. It might be possible to construct a physical theory that works the way you describe, I don't know. But in reality, when light speeds up or slows down, its wavelength changes in such a way as to keep the frequency (and energy) constant. For example, this happens to a light wave exiting a piece of glass (prism, window, etc.) and entering a region filled with air.

So for a given amount of energy to be expressed as a particular wavelength of light, wouldn't the speed of the waves have to be such that the correct amount of energy was delivered in the amount of time it took the waves to be emitted?

If I understand you correctly, this would mean that as long as the wavelength of light remains constant, the speed also has to remain constant? That's definitely true. But if I've misunderstood, please clarify.

Where I get stuck is what the relationship is between the inertia of an electron and the distance between the electron and nucleus. It seems like this would be the key to establishing a relationship between the speed of light and distance as we measure it according to material volume.

Well... I'm not sure if this is what you're getting at, but according to quantum mechanics, in a hydrogen atom in its lowest-energy state, the "average" (technically root mean square expectation value) of the electron's distance from the nucleus is given by the formula
a_0 = \frac{\hbar}{mc\alpha}
This is called the Bohr radius. As you can see, it does involve the mass of the electron, which is basically what physicists mean when they say "inertia". It also does involve the speed of light, but it's there as a unit conversion factor, not because of something involved that actually moves at the speed of light.

Anyway, I'm curious to see where you're going with that last point. (But not right away, I'm tired :zzz:)

 

[brainstorm]

I definitely agree that something without inertia shouldn't sensibly be able to change its speed. But regarding the second sentence, remember that for massless particles, momentum is completely independent of velocity. Having any certain amount of momentum doesn't tell you anything about the velocity. Although, I suppose your reasoning is fine as an intuitive argument. If it helps you make sense of the fact that photons always travel at speed c, by all means go ahead and use that as a memory aid to yourself.

No, I wasn't reasoning about logical memory aids. I was trying to establish a logical reason why a certain amount of momentum/energy would result in a certain wavelength with constant velocity. It does seem logical that energy would be expressed as wave frequency if velocity was a given, but that still doesn't answer the question of why the velocity is given at the speed it is given.

That is the fundamental question, isn't it... I don't think physics has an answer for that. I mean, if you want to know why it's 299792458 m/s, that's because of the way our particular units (the meter and the second) are defined: people chose a random distance to call the "meter" and a random time interval to call the "second", and it just turned out that the speed of light was 299792458 m/s. (Originally that was only approximate, then the meter was redefined to make that number exact)

This is too arbitrary. It would be nice to have a reason that correlates to the relationship between momentum and some force, e.g. electron momentum and strong nuclear force. I.e. something should explain the relationship between electron-nuclear-gravitation and the speed of light in a vacuum because otherwise there is no logical relationship between force, energy, and space. Material motion and radiation propagation are related in the speed of light, so there must be some logical relationship between matter and energy that explains the relationship.

Personally I would even say it's kind of meaningless, because the laws of physics themselves only seem to select one "natural" system of units, the Planck units, and in those units the speed of light is necessarily 1. But I guess that's getting into speculation - it's just my opinion, and as far as I know there's no consensus on this. (Most people probably don't even think about it)

Planck units have something to do with the minimum amount of energy transferred by a given frequency of radiation, which in turn seems to have something to do with the amount of energy released by a unit of electron motion change, right? So, this seems to have something to do with the inertia of the electron vis-a-vis the attractive force of a proton, no?

Be careful there, force and energy are different quantities. The mass of the electron multiplied by its acceleration is the force exerted by whatever is making the electron move, but that's not necessarily related to the amount of EM energy it radiates. In order to calculate the energy, you need a different formula, the Larmor formula:
P = \frac{e^2a^2}{6\pi\epsilon_0 c^3}

Interesting. This makes me wish I could read equations better qualitatively. This equation looks like the result of loads of data processing and attempts as fitting the data with predictive equations. Or was there a eureka moment of qualitative logic in there somewhere?

but if you were to look at the individual collisions, they'd seem pretty random. It's only when you put a large number of them together that you see a pattern in the frequencies.

How could it be random? Some factor must govern why and how a molecule "decides" whether to transfer KE to another molecule via contact or radiation, no?

No, you're right, atomic electrons do only undergo discrete jumps between energy levels. What I was talking about with the oscillations was a free electron, e.g. in an antenna, that is being pushed back and forth along a straight line (the antenna) in a sinusoidal motion.

aha, thanks. I didn't know how an electron could travel a distance corresponding to the length of a radio wave, but I can see how a free electron in an antenna could.

If I understand you correctly, this would mean that as long as the wavelength of light remains constant, the speed also has to remain constant? That's definitely true. But if I've misunderstood, please clarify.

I'm not sure, but it seems to me that time is relative to the wave, because the wave has no fixed time interval in and of itself. So the wavelength can vary according to how the time interval is defined. If a second is longer, red-shifted light would contain the same number of waves as its pre-shift predecessor, right? If that second is constant, then the red-shifted light would contain less waves-per-second (lower frequency) than its predecessor, right? How would red-shift be distinguishable from the light slowing down within a constant time interval? If all light waves shifted by the same amount, how would the shift be identifiable as a frequency-shift and not a velocity-shift? The only reason, I guess, would be the inability of the waves to decelerate due to lack of inertia.

Well... I'm not sure if this is what you're getting at, but according to quantum mechanics, in a hydrogen atom in its lowest-energy state, the "average" (technically root mean square expectation value) of the electron's distance from the nucleus is given by the formula

I have read that in QM electron position is probabilistic, but that is imo like saying human height is variable. In other words, I don't think it changes the mechanics of how any given electron interacts with its nucleus. I think it's just impossible to specify the exact parameters, such as the exact mass of a given electron, the exact mass of its corresponding nucleus, etc. Maybe I shouldn't think in terms of specific particles like this, but I can't think in general patterns of multiple particles without considering the behavior of each individual in relation to its own surroundings.

 

[Dale]

Light does have inertia (momentum).