Why does light travel at the speed it does?

[kenimpzoom]

Is there a specific reason that light travels at the speed it does (in a vacuum)? Something to do with photon size, wavelengths, etc, etc (This may be totally incorrect terminology, I am not really a physics guy, but I always like to learn).


This is more of a philosphy type question, so mods feel free to move it if you agree.

Thanks, Ken

[mathman]

The speed of light (in vacum) is constant, i.e. independent of wavelength or any other property of photons (there is no concept of "size"). For the answer to Why?, see "The Charge of The Light Brigade".

[Ebolamonk3y]

\frac{1}{\mu\epsilon}=c :) Find out why that is.

[KingNothing]

Another way of interpreting it and answering would be to say that light moves at the speed it does because of the constants we have chosen as far as what a meter is and what a second is.

[Nereid]

Is there a specific reason that light travels at the speed it does (in a vacuum)? Something to do with photon size, wavelengths, etc, etc (This may be totally incorrect terminology, I am not really a physics guy, but I always like to learn).


This is more of a philosphy type question, so mods feel free to move it if you agree.

Thanks, KenWelcome to Physics Forums kenimpzoom!

This question has been asked many times, both in the General Physics sub-forum, in Theory Development, and in Special & General Relativity. There are quite a few threads with, at times, lively discussion of this question.

My personal take: there is a theory (special relativity, SR for short) which postulates that c is a constant. All observations and experiments done to date have results that are consistent with SR, within its domain of applicability. Further, SR is a special case within a more general theory, general relativity (GR). All observations and experiments done to date have results that are consistent with GR, within its domain of applicability. Since GR is so well tested, and so broad in its scope, we can treat c as a physical constant, for a wide range of purposes (including the defining of the metre). There's also a great deal of history - where did the concepts which lead to SR come from? the role which Maxwell's and Lorentz' equations played, etc.

Then there's "what's *really* happening? what's the underlying *reality*??" Many folk here at PF have views and opinions on these questions, and they make their cases with varying degrees of precision, clarity, and (commonly) emotion.

However, IMHO, the discussion you're interested in having is better had in philosophy than physics.

[kenimpzoom]

Thanks guys. I was hoping there was a quick answer, but there are so many things out there that we dont understand yet.

Yall keep trying and one day, we'll get it all.

Ken

[Martin]

The short answer is “It just does.”

Ever since scientists discovered that light moved like waves in a vacuum—similar to sound waves in air, and water waves in water—they assumed that there was an all-pervading substance (they called it “ether”) that “carried” light waves, analogous to the the way that air carried sound waves via vibrating air molecules, and that water carried water waves via vibrating water molecules. In other words, the mysterious ether was what was “waving” or “vibrating” to carry the light along.

This implied that the speed of light would—like the speed of sound in air and the speed of water waves in water—depend upon the speed of the light source (for example, a flashlight) in the ether. However, all attempts to detect the ether as well as all attempts to determine differences in the speed of light due to the motion of the light source failed. While many scientists assumed that these failures were due to the lack of precise-enough measurements or experimental errors, Einstein postulated that perhaps the speed of light was a constant, independent of the motion of the source of the light. He assumed that the experimental evidence was, in reality, a demonstration of a fact of nature. He didn’t ask “why” it was true that the speed of light appeared to be a constant, he just accepted the experimental evidence as “proof” that it was. From this, he was able to create his Special Theory of Relativity.

(NOTE: In 1916, Einstein wrote a very easy-to-follow explanation of relativity theory, targeted to the non-scientist, which (I just discovered) is available in an online version. (See Relativity: The Special and General Theory) (http://www.bartleby.com/173/).)

[stevenb]

... there are so many things out there that we dont understand yet.

Yep, you get it!

[Fizex]

Hello PF, I think the more important question is not the variability of the speed of light, for it is known to be constant, but why it is at the value it is. Why does light travel at its speed and not a faster or slower constant? Is this a fundamental property of space or the photon? What is hindering light from propagating faster?

[DaleSpam]

Another way of interpreting it and answering would be to say that light moves at the speed it does because of the constants we have chosen as far as what a meter is and what a second is.That is my interpretation also. The dimensionful universal constants are a reflection of our completely arbitrary choice of units, not a reflection of physics.

[HallsofIvy]

Another way of interpreting it and answering would be to say that light moves at the speed it does because of the constants we have chosen as far as what a meter is and what a second is.

That is my interpretation also. The dimensionful universal constants are a reflection of our completely arbitrary choice of units, not a reflection of physics.

The specific value, in a specific system of units, does, obviously, but I doubt that was the intent of the question. I think the question was, rather, "why does light travel at this specific speed", not referring to its value in a given system of units.

[DaleSpam]

What does it even mean for something to have a "specific speed" without a system of units? How do you even speak of any dimensionful value without a system of units? You can certainly compare the speed of light to other speeds and get a dimensionless number which is independent of the choice of units, but as a dimensionful constant it has no meaning independent of the choice of units.

[jtbell]

The choice of measuring units is of course arbitrary, but after choosing a particular set of units and sticking with that set for the sake of discussion, is it not meaningful to ask, "why does light take a certain amount of time to travel between the earth and the moon, and not twice that amount?" (or a hundred times that amount, or one-millionth of that amount?)

We could make the unit of time the (average) period between two of my heart-beats. Why does a light pulse make a round trip from the earth to the moon and back, in the time of five of my heart-beats (just guessing here), and not ten, or one hundred of them?

As far as I know, there is no ultimate answer (yet) to this question.

I think we should interpret the original (five-year-old!) question this way, rather dive off into philosophy of measurement units.

[stevenb]

What does it even mean for something to have a "specific speed" without a system of units? How do you even speak of any dimensionful value without a system of units? You can certainly compare the speed of light to other speeds and get a dimensionless number which is independent of the choice of units, but as a dimensionful constant it has no meaning independent of the choice of units.


The question that is being asked is a simple one. In any system of units, why is the value of c the number it is and not double or not half or not any other scale factor off from that number?

The bottom line is that we do not know why.

Personally, I would start with a simplified question. Does modern physics provide an explanation of why the speed of light is not infinite?

[Lsos]

That is my interpretation also. The dimensionful universal constants are a reflection of our completely arbitrary choice of units, not a reflection of physics.

This might be missing the spirit of the question. I don't think anybody is interested in the the actual number, but in the way this number relates to other objects. If somebody at an air show asks "how does a jet fighter fly so fast!?" the appropriate answer would not be "because of the arbitrary value we assigned to units".

[RK1992]

Say if we set up a line of unstable atoms. We could ask "why does a beam of light travelling alongside these atoms go past an average of n atoms in the average separation in time between atoms decaying?". These are very natural units but we still don't see any real reason.

It's a weird question, really. "It just does" seems like a perfectly good answer but then we ask "why?" again.

It's like when you wind up your parents:
"Why can't I have it?"
"I don't have the money"
"Why?"
"Because I don't have a well paid job"
"Why?"
"Because I didn't try hard in school"
"Why?"
"Because I'm lazy"
"Why?"
"Maybe I have a combination of genes causing laziness?"
"Why?"
"Because my DNA is a pretty random cocktail of my mum's and dad's"
"Why?"
"Just is.. it's how it works."
"Why?"
*Smack*

Is there ever going to be an ultimate asnwer? We can keep asking "why?" but is there a time when such questions become worthless and we have to accept it as it is? For me (an A level student so not yet equipped to answer properly using any complex maths I'm afraid), it seems like a question for philosophy because physics usually asks "what happens?" as far as I can tell. Maybe human brains could never understand why? Maybe we were never equipped with the potential to answer the question.

[stevenb]

Is there ever going to be an ultimate asnwer? We can keep asking "why?" but is there a time when such questions become worthless and we have to accept it as it is? For me (an A level student), it seems like a question for philosophy because physics usually asks "what happens?" as far as I can tell.

You definitely make some good points. Still, thinking as physicists, we can be hopeful that a theory may one day be developed that is general enough to predict the value of c. Many of our theories can't exactly predict numbers like universal constants, or masses/charges of fundamental particles, and we are forced to determine them experimentally. However, this is not proof that it is impossible to do so eventually.

As an example, one can use quantum field theory to predict the size of a proton. This value seems to agree with previous experimental values. However, recently we see some data that shows the proton might be a little smaller. So, is the theory wrong, or was the calculation done incorrectly, or is the new experimental technique flawed? Not being an expert, I don't know, but I can look at this as an example of how a theory might predict numbers that were previously only given by experiment. A theory that is correct and very general, might give accurate numerical predictions for universal constants.

An interesting thing, which falls short of the goal here, can be found in classical electromagnetic theory. We can do simple electrostatic experiments and find a value of permitivity of free space \epsilon_0, then we can do a magnetostatic experiment to find the permeablity of free space \mu_0. Then, we can use Maxwell's equations to derive a wave equation which predicts the number for c as {{1}\over{\sqrt{\epsilon_0 \mu_0}}}. This is quite profound because some simple static measurements that anybody can do in their basement, can let us calculate an important universal constant related to a universal theory of electrodynamics, relativity and gravity. This still falls short of the goal, because we have just substituted a different universal constant for c. A deep analsysis reveals that permitivity and permeability are related based on choice of units and the required rules of coordinate transformations of the components of the electromagnetic field tensor. However, even though the ratio of them is known theoretically, the product of these constants can not be predicted by any physics theory. In effect, we can determine any two of the three constants, \mu_0, \epsilon_0, c, once the third is given to us by experiment. Development of a theory that can predict all three values, as required by a universal law, would be a major achievment in physics.

[JDługosz]

Whatever the speed is, the point is that there is a special finite speed that is an absolute and limiting velocity through space-time. Whether that actual value was higher or lower would not change the discussion.

Consider pushing an object. The lighter the object, the faster it gets, with a given energy. What happens in the limit? As the inertia approaches zero, the object takes off at high speed with the slightest force. At zero, it must travel at that maximum speed. That is easily seen as consistent with the limit as inertia approaches zero.

[JDługosz]

Development of a theory that can predict all three values, as required by a universal law, would be a major achievment [sic] in physics.

I was just thinking about that last night, before finding this post.

I'm thinking that the "speed c" (yes light travels at that speed, but I mean the deeper principle) is not unit-less so is not a proper fundamental constant. But, it has meaning in a sense of defining the way space and time mix. The only meaning comes when other things are related to it. You can simply call it "1", and decide that it's large compared to molecular reactions and so on.

It's not c that's interesting; it's the speed of everything else, which can be expressed in terms of c.

We shouldn't worry about why c is the value it is. It is 1. Rather, you should wonder why mosquitoes fly the particular speed they do (e.g. 4 nano c). Rather than marveling at the particular value of mass-energy equivalence, just realize that it is 1, and wonder why the chemical energy in a firecracker is the value it is, measured in those terms.

[Pythagorean]

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).

Interestingly, I read a paper in the last couple years about reaming gauge symmetry, and that the faster you accelerate , the smaller your field of vision. I will dig up the paper if I can, it was from the European space agency.

[Pythagorean]

OK, it's called "drame dragging". Here's the paper where I first heard of it. I'm still learning about it, so I may have misunderstood it:

Tajmar, Martin et al. Experimental Detection of the Gravitomagnetic London Moment. (easy google).

[pallidin]

Do you mean "frame dragging"?
A very interesting phenomenon.

[DaleSpam]

The question that is being asked is a simple one. In any system of units, why is the value of c the number it is and not double or not half or not any other scale factor off from that number?

The bottom line is that we do not know why. No, we know exactly why. It is that value because we chose our units such that it had that value.

The thing that most people don't realize is that the values of the universal dimensionful constants (e.g. c, h, G) have no measurable impact on physics whatsoever. The only universal constants which have measurable impact on physics are the dimensionless ones (e.g. the fine structure constant). In fact, if you were to vary the dimensionful constants such that c actually doubled but none of the dimensionless constants changed then you would not even be able to detect the change in c. See:

http://www.physicsforums.com/showpost.php?p=2011753&postcount=55
http://www.physicsforums.com/showpost.php?p=2015734&postcount=68


Personally, I would start with a simplified question. Does modern physics provide an explanation of why the speed of light is not infinite?This is, IMO a much better question. It is one of the fundamental symmetries of the universe, and modern physics seeks to describe everything in terms of symmetries but does not seek to explain why the universe has these symmetries.

Another better question than the original question is "why does the fine structure constant have the value that it does". That is a question that does not depend on units and has an unambiguous and measurable impact on physics. AFAIK it is unanswered by current theories, but the hope is that a working TOE will have fewer (or even 0) fundamental dimensionless constants. See:

http://math.ucr.edu/home/baez/constants.html

[HallsofIvy]

No, we know exactly why. It is that value because we chose our units such that it had that value.
You keep repeating this as if it meant something. Everyone knows that the specific numeric value of a physical constant depends on our choices of units. But that is irrelevant to the question! The real question here is "Why is the speed of light constant", NOT "why does it have this specific value".

The thing that most people don't realize is that the values of the universal dimensionful constants (e.g. c, h, G) have no measurable impact on physics whatsoever. The only universal constants which have measurable impact on physics are the dimensionless ones (e.g. the fine structure constant). In fact, if you were to vary the dimensionful constants such that c actually doubled but none of the dimensionless constants changed then you would not even be able to detect the change in c. See:

http://www.physicsforums.com/showpost.php?p=2011753&postcount=55
http://www.physicsforums.com/showpost.php?p=2015734&postcount=68


This is, IMO a much better question. It is one of the fundamental symmetries of the universe, and modern physics seeks to describe everything in terms of symmetries but does not seek to explain why the universe has these symmetries.

Another better question than the original question is "why does the fine structure constant have the value that it does". That is a question that does not depend on units and has an unambiguous and measurable impact on physics. AFAIK it is unanswered by current theories, but the hope is that a working TOE will have fewer (or even 0) fundamental dimensionless constants. See:

http://math.ucr.edu/home/baez/constants.html

[stevenb]

No, we know exactly why. It is that value because we chose our units such that it had that value.


I understand much of what you are saying, but it seems to me that you're still not addressing one aspect of the question. If we choose SI units, we get a number for c close to 3,000,000 km/s. So, why is it not 4,900,000 km/s, or 2 km/s?

I have never seen a theory that explains this. If you "know exactly why", then please explain it. You seem to be implying that c is arbitrary and that no matter what finite value it has (as long as it is not infinite or zero) all physical theories and our interpretation of observations will scale in a way the makes the change unnoticable. In fact, you are saying that it is so unoticable that even our interpretation of the meter and the second will allow us to get the same number for c. This does not seem right to me.

For example, for this to be true, a doubling of c would need to scale the dimensions of a hydrogen atom proportionally, or effect time somehow.

Or, put another way, the fact that light can travel a certain number of cesium atominc radii in one period of oscillation of the cesium atom microwave spectral line, seems to set a scale that is not arbitrary.

If I'm wrong, then please explain how the scaling of all known physical laws (GR, QFT, QM, EM) makes c arbitrary. If tomorrow I do an experiment and find that the distance traveled in one oscillation of cesium is twice the number of cesium atomic radii as today, then I'm going to say that there is something significant (and unexpected) happening to the universe.

[DaleSpam]

You keep repeating this as if it meant something. Everyone knows that the specific numeric value of a physical constant depends on our choices of units. But that is irrelevant to the question! The real question here is "Why is the speed of light constant", NOT "why does it have this specific value".There are essentially three questions you can ask about the speed of light:
1) Why does it have the value it does?
2) Why is it finite?
3) Why is it frame-invariant?

The first is, as I responded, because of our choice of units and no other reason. I think that it has more meaning than you admit because it leads to an improved understanding of measurements, units, and the dimensionless constants. I also think that it is not obvious to most people.

The second and third are both because of the Poincare symmetry of the laws of nature. This is basically a tautology since the Poincare symmetry means that there is a finite frame-invariant speed.

So it begs the follow-up question: "Why are the laws of nature Poincare symmetric?". Which is not answered by any modern theories AFAIK and is taken as a fundamental fact of nature along with the other symmetries and the fundamental dimensionless constants.

[DaleSpam]

You seem to be implying that c is arbitrary and that no matter what finite value it has (as long as it is not infinite or zero) all physical theories and our interpretation of observations will scale in a way the makes the change unnoticable. In fact, you are saying that it is so unoticable that even our interpretation of the meter and the second will allow us to get the same number for c. This does not seem right to me.

For example, for this to be true, a doubling of c would need to scale the dimensions of a hydrogen atom proportionally, or effect time somehow. Did you read the links I posted previously:

http://math.ucr.edu/home/baez/constants.html
http://www.physicsforums.com/showpost.php?p=2011753&postcount=55
http://www.physicsforums.com/showpost.php?p=2015734&postcount=68

In the links to my posts I address exactly your question in quite some detail.

[stevenb]

In the links to my posts I address exactly your question in quite some detail.

No disrespect intended, but your posted references do not exactly address my question to my satisfaction. As I said above, I understand much of what you are saying and I don't disagree with anything you've referenced. However, you seem to miss the fundamental point I'm trying to make.

If I measure the speed of light to be the traversing of X number of cesium atomic radii (0.26 nm) during one transition of the cesium microwave line (1/9192631770 of a second), that speed has a physical meaning, even if the number itself does not. The number does not mean anything because I could use different units, but the speed itself has meaning in that it can be related to two atributes (dynamic and spatial) of the cesium atom. Those attributes are the result of quantum physics, the values of e and h, and much more.

If tomorrow I were to measure 10X instead of X, and assuming that the experiments were done correctly, I would need to conclude that a significant change in physical laws (as I understand them) occured overnight. From your points I would conclude that the fine structure constant has changed, but the change is meaningful.

Now lets say that c changes and then electron charge and Planks constant also change so that the fine structure constant is the same. Are you confident enough to say that all physics on the atomic scale and on the cosmological scale will look identical and the end result is that I will still measure c to corresponde to X number of ceasium atomic radii (0.26 nm) during one transition of the ceasium microwave line, and that light will still take about 4 years (by reckoning with my new measure of time) to reach Alpha Centuri? The references you gave do not prove this point. If you believe this point, and can demonstrate it, I would be very grateful to have learned something significant from you. Proving this would demonstrate that the three values e, h and c are arbitrary and only the net effect of the fine structure constant is significant. This would be proof that you are correct in your assertion. If instead, you mearly show that you have 3 (or more) dimentionless constants that are used to determine e, h and c, then I won't be impressed, since you are just begging the question.

[DaleSpam]

No disrespect intended, but your posted references do not exactly address my question to my satisfaction. As I said above, I understand much of what you are saying and I don't disagree with anything you've referenced. However, you seem to miss the fundamental point I'm trying to make.That may be so, I think the post exactly answers the question, so there must be some misunderstanding on one side or the other. Let me see if I can address it here.


If I measure the speed of light to be the traversing of X number of ceasium atomic radii (0.26 nm) during one transition of the ceasium microwave line (1/9192631770 of a second), that speed has a physical meaning, even if the number itself does not. The number does not mean anything because I could use different units, but the speed itself has meaning in that it can be related to two atributes (dynamic and spatial) of the ceasium atom. Those attributes are the result of quantum physics, the values of e and h, and much more.

If tomorrow I were to measure 10X instead of X, and assuming that the experiments were done correctly, I would need to conclude that a significant change in physical laws (as I understand them) occured overnight. From your points I would conclude that the fine structure constant has changed, but the change is meaningful.Yes, exactly. The fine structure constant changed, which change resulted in a measurable change between the length of a meter as determined by the speed of light and the length of a meter as determined by a "meter stick" made out of a bunch of cesium atoms in a line. A cesium atom is about 5 Bohr radii in diameter, so that is why I included the section about the Bohr radius in my first post referenced above. Does that help show the connection between what you are asking and what I wrote?


Now lets say that c changes and then electron charge and Planks constant also change so that the fine structure constant is the same. Are you confident enough to say that all physics on the atomic scale and on the cosmological scale will look identical I did not actually vary the electron charge nor mass in my simulation, but I did vary c, G, h, and the vacuum permittivity. But yes, with the results from doing that I am indeed confident in general that the physics would look identical if the dimensionful constants are varied in such a way as to leave the dimensionless constants unchanged.


The references you gave do not prove this point. If you believe this point, and can demonstrate it, I would be very grateful to have learned something significant from you. Proving this would demonstrate that the three values e, h and c are arbitrary and only the net effect of the fine structure constant is significant. This would be proof that you are correct in your assertion.I have a Mathematica notebook with all of the calculations. I summarized the results in my second post referenced above, but if you have Mathematica then I would be more than glad to share the notebook with you so that you can look at my calculations and make your own modifications and conclusions.


If instead, you mearly show that you have 3 (or more) dimentionless constants that are used to determine e, h and c, then I won't be impressed, since you are just begging the question.No, I varied 4 dimensionful constants (c, G, h, vacuum permittivity) and found that the physical measurements were functions only of the two dimensionless constants (fine structure constant and the gravitational coupling constant) that I studied. In any case, I don't think it is possible to write any dimensionful constant in terms of dimensionless constants, although you can certainly go the other way.

[stevenb]

A cesium atom is about 5 Bohr radii in diameter, so that is why I included the section about the Bohr radius in my first post referenced above. Does that help show the connection between what you are asking and what I wrote?

Yes it does.


... yes, with the results from doing that I am indeed confident in general that the physics would look identical if the dimensionful constants are varied in such a way as to leave the dimensionless constants unchanged.

With your confidence and no objections coming from anyone else, I'm inclined to agree momentarily and look further. Just looking at frequencies scaled by the Rydberg constant and distances relative to the Bohr radius, some quick checks are working out for variations of e, h, c and epsilon. My intuition is throwing up some red flags, so I'd want to dig deeper before I'm comfortable, but I appreciate your response.


I have a Mathematica notebook with all of the calculations. I summarized the results in my second post referenced above, but if you have Mathematica then I would be more than glad to share the notebook with you so that you can look at my calculations and make your own modifications and conclusions.

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


In any case, I don't think it is possible to write any dimensionful constant in terms of dimensionless constants ...

Good point, and this is actually one of a few things that bothers my intuition, but I'll get to grips with it.

[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:
Nothing but Relativity (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.....

[DaleSpam]

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:
http://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:
http://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 dimentionless 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, o:) 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)

[DaleSpam]

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 dimentionless 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 travelled 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 travelled 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 :tongue2: (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, mrel = E/c^2. Using that concept, you could write the momentum of a photon as p = mrelc, and the momentum of a massive particle (which I mentioned above) as p = mrelv. 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 :tongue2: (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 :wink:

[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 travelled 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? :rofl: 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 :wink:
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 (http://en.wikipedia.org/wiki/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 (http://en.wikipedia.org/wiki/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 (http://en.wikipedia.org/wiki/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.

[DaleSpam]

Light does have inertia (momentum).

[diazona]

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.
OK, well, here's a reason why a certain momentum/energy corresponds to a certain wavelength: perhaps you know that a light wave is made up of oscillating electric and magnetic fields. So when this wave hits (and is absorbed by) a (free-ish) charged particle, the electromagnetic field will cause the particle to move around. If the particle is confined to a straight line (like an antenna) parallel to the electric field, it will oscillate in a sine wave; if it's completely free, it may undergo some more complicated motion.

Anyway, the higher the frequency of the radiation, the faster the EM field oscillates, and thus the faster the particle will move. If the particle moves faster, it has more energy; therefore energy is directly related to frequency. (This argument doesn't tell you that energy is proportional to frequency, just that when one gets bigger, so does the other)

Also, the higher the frequency of the radiation, the less time it takes for one complete cycle of the wave to pass through a given point. Assuming that the wave moves at a constant speed, if it takes less time for one cycle of the wave to pass through a point, the distance covered by one cycle of the wave (i.e. the wavelength) will be shorter. Thus higher frequency correlates to shorter wavelength; frequency is inversely related to wavelength. (This argument doesn't tell you that frequency is inversely proportional to wavelength, but if you know that velocity = distance / time it's pretty straightforward to figure out)

Combining the conclusions from the previous two paragraphs:
high energy = high frequency = short wavelength
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.
What, like E=mc2? :wink: (actually E2 = m2c2 + p2c4) Although I doubt that that's the relationship you're looking for - it's another equation where the speed of light enters only as a unit conversion factor.

I don't mean to sound patronizing, but it really sounds like you're grasping at straws here. I don't know of anything that could be the relationship you're talking about and I don't even understand why you think there has to be one.

And the number 299792458 that humanity has chosen to represent the speed of light in SI units is arbitrary, no way around it, because our choice of units is arbitrary. Just look at how many different unit systems there are in the world: SI, CGS, imperial, atomic, astronomical, cosmological, probably plenty that I've never heard of...
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?
No, no, that's Planck's constant. Planck units (http://en.wikipedia.org/wiki/Planck_units) are a system of units (like SI units) that are based only on the properties of free space, and thus in some sense are the most "fundamental" or "natural" units to do physics in.
So, this seems to have something to do with the inertia of the electron vis-a-vis the attractive force of a proton, no?
No, I don't see how that comes into it at all.
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?
There are two detailed derivations of the equation in the Wikipedia article I linked to. This was not a result of data analysis, nor was it a random inspiration - its origins are well-grounded in electromagnetic theory.
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?
Nope. There really is random chance at work at the most basic level of interparticle interactions. Quantum mechanics specifies that, to put it very simply, in situations where multiple outcomes are allowed by the laws of physics, there is no factor that predetermines which outcome will actually occur. Collisions between particles are of this sort; there are a few restrictions imposed by the laws of conservation of momentum and energy, but within the possibilities allowed by those, it's a random choice.

Note that quantum effects are small, so they're most noticeable on very small scales, generally the size of an atom and smaller (roughly speaking). When you work up to molecules, once you take into account the orientation and relative position of the molecules as they collide, often one possible result becomes overwhelmingly more likely than the others.
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.
OK, cool :cool: But actually how far the electron travels really determines the amplitude of the wave (more or less), and how fast it travels determines the frequency (and thus wavelength). It's possible to arrange for an electron to travel a long distance really fast (large amplitude, short wavelength) or a short distance really slowly (small amplitude, long wavelength).
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?
Well, you don't use the same wave whose frequency you're trying to measure to define the unit of time! If you did that, then the wave would always appear to have the same frequency. But you would find that other physical processes, which normally always take a specific time, would take longer or shorter, and it'd be difficult or impossible to develop a consistent physical theory.
If that second is constant, then the red-shifted light would contain less waves-per-second (lower frequency) than its predecessor, right?
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?
Because other time standards (besides light waves) don't change. For example, an atomic clock. You can set up an atomic clock and a ruler next to a redshifted wave and use them it to measure the wave's frequency and wavelength respectively, and you will always find that the wave travels at the speed c = 299792458 m/s. But you may find that its frequency has changed relative to some other location where you did the same measurement.
The only reason, I guess, would be the inability of the waves to decelerate due to lack of inertia.
Well, as DaleSpam pointed out, light actually does have inertia, because it has energy. I've been sort of glossing over that point.
I have read that in QM electron position is probabilistic, but that is imo like saying human height is variable.
That's what everybody thinks at first, but it's really not the same. The true probabilistic nature of QM takes some getting used to.
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.
I'm not quite sure what you're getting at with this...

[brainstorm]

Combining the conclusions from the previous two paragraphs:
high energy = high frequency = short wavelength
Great explanation, but I knew this.

What, like E=mc2? :wink: (actually E2 = m2c2 + p2c4) Although I doubt that that's the relationship you're looking for - it's another equation where the speed of light enters only as a unit conversion factor.
I've actually been figuring this out via another thread that discusses the units for measuring momentum in comparison to energy.

I don't mean to sound patronizing, but it really sounds like you're grasping at straws here. I don't know of anything that could be the relationship you're talking about and I don't even understand why you think there has to be one.
Couldn't you look at an atom/molecule as a tiny radio transmitter? If so, wouldn't the diameter of the electron orbit determine the amplitude of waves emitted? If the amplitude was fixed, wouldn't the wavelength also be fixed according to the rate at which the electron oscillated around the nucleus, which would be determined by the force-distance ratio between the nucleus and electron? If amplitude and frequency were determined in this way, wouldn't the velocity of the waves be the result of how much energy was expressed in the wave? I.e. if the wave travelled any faster or slower with the same frequency and amplitude, wouldn't it transmit a different amount of energy than it was originally endowed with?

And the number 299792458 that humanity has chosen to represent the speed of light in SI units is arbitrary, no way around it, because our choice of units is arbitrary. Just look at how many different unit systems there are in the world: SI, CGS, imperial, atomic, astronomical, cosmological, probably plenty that I've never heard of...
Fine, units are arbitrary. But whatever physical mechanics that governs the speed of light relative to, say, gravitation wouldn't be, would it?

Nope. There really is random chance at work at the most basic level of interparticle interactions. Quantum mechanics specifies that, to put it very simply, in situations where multiple outcomes are allowed by the laws of physics, there is no factor that predetermines which outcome will actually occur. Collisions between particles are of this sort; there are a few restrictions imposed by the laws of conservation of momentum and energy, but within the possibilities allowed by those, it's a random choice.
Well, it seems to me that energy transfers due to collisions are not that distinct from those transferred through radiation. Maybe the big difference is that the energy transferred during a collision involves a disturbance in the relationship/distance between the electrons and the nucleus. Actually, that doesn't make sense because the electrons change distance from the nucleus when absorbing or emitting radiation, too right? So what IS the difference between two particles bouncing off each other or the electrons bouncing an EM wave to another particle that receives it as momentum?



Because other time standards (besides light waves) don't change. For example, an atomic clock. You can set up an atomic clock and a ruler next to a redshifted wave and use them it to measure the wave's frequency and wavelength respectively, and you will always find that the wave travels at the speed c = 299792458 m/s. But you may find that its frequency has changed relative to some other location where you did the same measurement.
But why couldn't you just say that the atomic clock is measuring one time while the redshifted wave is actually existing at another time-rate, which it was emitted at?

Well, as DaleSpam pointed out, light actually does have inertia, because it has energy. I've been sort of glossing over that point.
Wouldn't that mean it would decelerate due to friction?

That's what everybody thinks at first, but it's really not the same. The true probabilistic nature of QM takes some getting used to.

I'm not quite sure what you're getting at with this...
I don't know what "true probabilistic nature" means. To me there are two ways of treating phenomena involving multiplicities. One is to recognize the individual elements in the multiplicity as being engaged in unique interactions, which nonetheless can be probabilistically predicted in terms of patterns. The other is to treat multiplicities as themselves collective entities, which I don't like to do because I find it confounding with regards to the behavior of elements at the individual level.

[diazona]

Great explanation, but I knew this.
OK, sorry. I kind of have to guess at what you know and don't know :wink:
Couldn't you look at an atom/molecule as a tiny radio transmitter? If so, wouldn't the diameter of the electron orbit determine the amplitude of waves emitted? If the amplitude was fixed, wouldn't the wavelength also be fixed according to the rate at which the electron oscillated around the nucleus, which would be determined by the force-distance ratio between the nucleus and electron?
For a while (up until the early 1900s) this is exactly what people thought, and it is what you'd expect based on classical mechanics. But it doesn't correspond to reality - experiments and theoretical considerations show that atoms don't give off radiation in this way, even though it seems like they should. This discrepancy was one of the main inspirations for quantum mechanics. See Wikipedia's article on the Bohr model (http://en.wikipedia.org/wiki/Bohr_model), for example.
If amplitude and frequency were determined in this way, wouldn't the velocity of the waves be the result of how much energy was expressed in the wave? I.e. if the wave travelled any faster or slower with the same frequency and amplitude, wouldn't it transmit a different amount of energy than it was originally endowed with?
No, it wouldn't. The amount of energy transferred is determined by the frequency and amplitude. Even if the wave got faster or slower, the amount of energy wouldn't change unless the frequency and/or amplitude changed.
Fine, units are arbitrary. But whatever physical mechanics that governs the speed of light relative to, say, gravitation wouldn't be, would it?
No, you're right. That's the part that physics doesn't have a good answer for. As I might have said already, a lot of people hope that a "theory of everything" would shed some light on this, but current theories don't provide any explanation. Plenty of people are trying to figure it out, of course.
Well, it seems to me that energy transfers due to collisions are not that distinct from those transferred through radiation. Maybe the big difference is that the energy transferred during a collision involves a disturbance in the relationship/distance between the electrons and the nucleus. Actually, that doesn't make sense because the electrons change distance from the nucleus when absorbing or emitting radiation, too right? So what IS the difference between two particles bouncing off each other or the electrons bouncing an EM wave to another particle that receives it as momentum?
Good insight, the two processes do work pretty much the same way. You actually can elevate an electron in an atom to a higher energy level (further away from the nucleus) by hitting it with another electron, just as you could by hitting it with an EM wave. The difference is that only the EM wave can be absorbed. In the other (former) case, the impinging electron would have to come back out, though possibly with less energy than it had going in.

Incidentally, if you look closely enough, two electrons will never actually collide, they'll just get really close to each other and then "bounce" back due to their electrical repulsion. The "message" of that electrical repulsion is transmitted by an EM wave.
But why couldn't you just say that the atomic clock is measuring one time while the redshifted wave is actually existing at another time-rate, which it was emitted at?
What do you mean by a time-rate?
Wouldn't that mean it would decelerate due to friction?
There is no friction at the level of subatomic particles (or EM waves). Friction actually arises from the electromagnetic interactions of large numbers of atoms, and it's related to the roughness of a physical surface.
I don't know what "true probabilistic nature" means.
Well, here's an attempt (probably not the greatest) to clarify what I meant by that. If you start with a large number of people with different heights, you can do all sorts of statistical stuff like determining the height distribution, and if you pick a random person and measure their height, you'll get a result equivalent to a random number taken from that distribution. But all the randomness comes from how you make your choice of person. Once you've picked out a person, everything is completely deterministic. You measure their height and get some result, and then you can measure it again and again and reliably get the same result. Or you could look at their health records (well, if you had access) and read off their height without actually measuring it.

For the quantum equivalent, consider a large number of hydrogen atoms that are in the ground state. Again, you can do statistical stuff like determining the distribution of the electron's orbital radius, and if you pick a random atom and measure its orbital radius, you'll get a result equivalent to a random number taken from that distribution. But unlike people, the result is not determined by your choice of atom! If you measure the orbital radius, then wait a little while and measure it again, you might get a completely different, random result. And if you measure it yet again, you might get another completely different, random result. Make enough measurements on the same atom and you'll eventually start to see the same distribution you got from the whole ensemble of atoms in the beginning.
To me there are two ways of treating phenomena involving multiplicities. One is to recognize the individual elements in the multiplicity as being engaged in unique interactions, which nonetheless can be probabilistically predicted in terms of patterns. The other is to treat multiplicities as themselves collective entities, which I don't like to do because I find it confounding with regards to the behavior of elements at the individual level.
Indeed, and you'll find both those viewpoints used in physics. (Way #1 is used in classical mechanics, basic quantum mechanics, classical electromagnetism, quantum field theory, etc. Way #2 is used in statistical mechanics, thermal physics, fluid dynamics, solid state physics, etc.)

[brainstorm]

No, it wouldn't. The amount of energy transferred is determined by the frequency and amplitude. Even if the wave got faster or slower, the amount of energy wouldn't change unless the frequency and/or amplitude changed.
But frequency literally means how many waves per unit time. So a wave slowing down takes longer to transmit the same number of waves, thus reducing the frequency.

Good insight, the two processes do work pretty much the same way. You actually can elevate an electron in an atom to a higher energy level (further away from the nucleus) by hitting it with another electron, just as you could by hitting it with an EM wave. The difference is that only the EM wave can be absorbed. In the other (former) case, the impinging electron would have to come back out, though possibly with less energy than it had going in.
Thanks. I don't see why you call the EM wave's absorption as a difference, though. If the EM wave is just carrying the energy of a distant electron that was its source, then its "absorption" is no different from the absorption of one electron's momentum by another during a collision, right?

Incidentally, if you look closely enough, two electrons will never actually collide, they'll just get really close to each other and then "bounce" back due to their electrical repulsion. The "message" of that electrical repulsion is transmitted by an EM wave.
I knew electrons repelled each other due to charge, but I'd never thought of this as an EM wave, but I guess it is an electric field in motion, isn't it? But since it remains attached to the electron, it travels slower than C, right?

What do you mean by a time-rate?
Um, in other words you could say that the wave slowed down and this is what caused it to appear redshifted to a clock that measured it in terms of a time faster than itself.

There is no friction at the level of subatomic particles (or EM waves). Friction actually arises from the electromagnetic interactions of large numbers of atoms, and it's related to the roughness of a physical surface.
Maybe friction is the wrong concept. What I was addressing was the earlier point that light doesn't decelerate or accelerate in being emitted or changing direction. I presume objects/particles do this because they are subject to work (force over distance) instead of themselves being work, as radiation seems to be. So radiation can't accelerate itself because it is a means to accelerate. Does this make sense?

If you measure the orbital radius, then wait a little while and measure it again, you might get a completely different, random result. And if you measure it yet again, you might get another completely different, random result. Make enough measurements on the same atom and you'll eventually start to see the same distribution you got from the whole ensemble of atoms in the beginning.
Right, this is where I wonder why physicists deem it necessary to have the electron(s) of particular particle behaving in regular patterned ways. To me it seems logical that electrons are constantly brushing by other electrons in their own particle and others, which causes them to shift motion and direction in all sorts of quirky (not quarky) ways. So, just because electrons don't follow a fixed trajectory doesn't mean their behavior isn't the result of mechanical determination. The electron interactions could just be very complex, making them seem chaotic.

Indeed, and you'll find both those viewpoints used in physics. (Way #1 is used in classical mechanics, basic quantum mechanics, classical electromagnetism, quantum field theory, etc. Way #2 is used in statistical mechanics, thermal physics, fluid dynamics, solid state physics, etc.)
I don't like statistical methods because they tend to substitute abstract/processed data for direct observational data. They also substitute automatic validity testing for reasoning-based analysis. There are numerous reasons I dislike statistics - it's mostly similar to the reason I like manual transmissions, windows, door locks, etc. more than automatic ones.

[diazona]

But frequency literally means how many waves per unit time. So a wave slowing down takes longer to transmit the same number of waves, thus reducing the frequency.
Not necessarily, because the wavelength can (and does) change. (Technical note: frequency is cycles per unit time)
Thanks. I don't see why you call the EM wave's absorption as a difference, though. If the EM wave is just carrying the energy of a distant electron that was its source, then its "absorption" is no different from the absorption of one electron's momentum by another during a collision, right?
Well, yeah. But the EM wave completely ceases to exist once it is absorbed by the atom. A colliding electron couldn't cease to exist.
I knew electrons repelled each other due to charge, but I'd never thought of this as an EM wave, but I guess it is an electric field in motion, isn't it? But since it remains attached to the electron, it travels slower than C, right?
No, it doesn't remain attached to the electron, and it does travel at the speed of light.
Um, in other words you could say that the wave slowed down and this is what caused it to appear redshifted to a clock that measured it in terms of a time faster than itself.
You could say that its frequency slowed down (i.e. got smaller), and that's what caused it to appear redshifted, sure. But that's totally different from saying that its speed slowed down.
Maybe friction is the wrong concept. What I was addressing was the earlier point that light doesn't decelerate or accelerate in being emitted or changing direction. I presume objects/particles do this because they are subject to work (force over distance) instead of themselves being work, as radiation seems to be. So radiation can't accelerate itself because it is a means to accelerate. Does this make sense?
Objects/particles accelerate because they have mass. That's pretty much all there is to it. I don't think I'd call radiation a means to accelerate, although maybe you could say that about the energy it carries. (Of course, particles can carry energy too)
Right, this is where I wonder why physicists deem it necessary to have the electron(s) of particular particle behaving in regular patterned ways.
We (they) do? Maybe I'm missing something...
To me it seems logical that electrons are constantly brushing by other electrons in their own particle and others, which causes them to shift motion and direction in all sorts of quirky (not quarky) ways. So, just because electrons don't follow a fixed trajectory doesn't mean their behavior isn't the result of mechanical determination. The electron interactions could just be very complex, making them seem chaotic.
Well, but what I was saying applies equally well if there's just one electron and one proton and nothing else (except the measuring apparatus), so you can't use interactions between particles as an excuse.

For the first 40 or 50 years of quantum mechanics, many people thought the same way you do, that the behavior of electrons was mechanically determined and that the apparent randomness they showed was just due to some sort of complex interaction or other factor that we weren't able to observe. In 1964, John Bell published a paper describing an experiment that could be performed on pairs of particles, together with a particular condition (Bell's inequality (http://en.wikipedia.org/wiki/Bell%27s_theorem)) that had to be satisfied by any physical model in which measurements are mechanically determined. The experiment was first performed in 1972 (http://en.wikipedia.org/wiki/Bell_test_experiments), and has been repeated many times since then, and the results violate Bell's inequality, thus proving that "mechanical determination" is insufficient to explain reality.
I don't like statistical methods because they tend to substitute abstract/processed data for direct observational data. They also substitute automatic validity testing for reasoning-based analysis. There are numerous reasons I dislike statistics - it's mostly similar to the reason I like manual transmissions, windows, door locks, etc. more than automatic ones.
If you're not a Linux user, you should be :wink: But that's not really what statistics is about. It's really about describing large amounts of data, and extracting useful information which you might never notice by looking at the individual values.

[brainstorm]

Well, yeah. But the EM wave completely ceases to exist once it is absorbed by the atom. A colliding electron couldn't cease to exist.
No, but my point is that the electron emitting the radiation doesn't cease to exist once its emission is absorbed by its destination particle. All I'm trying to say is that radiation is a teleported particle collision, for goodness sake!

No, it doesn't remain attached to the electron, and it does travel at the speed of light.
Huh? An electron's negative charge doesn't remain with the electron?

You could say that its frequency slowed down (i.e. got smaller), and that's what caused it to appear redshifted, sure. But that's totally different from saying that its speed slowed down.
How would you differentiate speed decreasing from frequency shift? How would speed-decrease of a beam consisting of waves be differentiated from a frequency decrease in the beam due to the waves stretching out?

Objects/particles accelerate because they have mass. That's pretty much all there is to it. I don't think I'd call radiation a means to accelerate, although maybe you could say that about the energy it carries. (Of course, particles can carry energy too)
Exactly, any expression of energy can be treated as a potential source of energy for another object/particle. Only, radiation isn't subject to deceleration or acceleration due to gravity, is it? I know gravity can change the direction of radiation, but not its momentum, right?

We (they) do? Maybe I'm missing something...
Well, why else would it be necessary to treat electron position probabilistically - if you didn't expect it to behave regularly in the first place?

Well, but what I was saying applies equally well if there's just one electron and one proton and nothing else (except the measuring apparatus), so you can't use interactions between particles as an excuse.
And nothing is interacting with the atom and its electron?

the results violate Bell's inequality, thus proving that "mechanical determination" is insufficient to explain reality.
I'll have to study this. Thanks.

If you're not a Linux user, you should be :wink: But that's not really what statistics is about. It's really about describing large amounts of data, and extracting useful information which you might never notice by looking at the individual values.
I acquired a distaste for statistics from social science. I'm aware of the claimed benefits of statistical modeling. I dislike them because they substitute empirical realities with means. They promote forms of thinking that avoid exploring the full range of interactive possibilities between individuals. This could be true of humans or particles, I assume.

[diazona]

No, but my point is that the electron emitting the radiation doesn't cease to exist once its emission is absorbed by its destination particle. All I'm trying to say is that radiation is a teleported particle collision, for goodness sake!
Right, I'll agree with that. (except: "teleported" always seems to give people the wrong impression, maybe I'd say "long-distance") I think we've been saying the same thing in different ways. I'm going to stop clarifying :wink:
Huh? An electron's negative charge doesn't remain with the electron?
I'm talking about the EM wave, not the charge. The EM wave doesn't remain with the electron, and it does travel at the speed of light. But the electron's charge does remain with the electron, and it doesn't travel at the speed of light.

The charge and the wave are not the same thing. You can think of the charge as the source that generates the wave, the same way a boat generates a wake.
How would you differentiate speed decreasing from frequency shift? How would speed-decrease of a beam consisting of waves be differentiated from a frequency decrease in the beam due to the waves stretching out?
As I've been saying, you'd directly measure the wave's speed and frequency. If the speed decreases, you'd see it in the measurement. If instead the frequency decreases, you'd see that in the measurement. (Technical point: I'd think of it as the frequency decrease causing the waves to stretch out, rather than the other way around.)
Exactly, any expression of energy can be treated as a potential source of energy for another object/particle. Only, radiation isn't subject to deceleration or acceleration due to gravity, is it? I know gravity can change the direction of radiation, but not its momentum, right?
You're right that radiation never changes its speed, even in the presence of gravity. But gravity actually can change the momentum (and energy) of radiation, in both magnitude and direction, because that momentum (energy) is related to the radiation's frequency, not its speed. This is called gravitational redshift (http://en.wikipedia.org/wiki/Gravitational_redshift).

Here's an example (based on an actual experiment (http://en.wikipedia.org/wiki/Pound–Rebka_experiment)): suppose you have a device that repeatably emits EM waves of a certain frequency, and put it at a certain height above Earth's surface. If you measure that frequency right next to the device, you'll get a certain result. Alternatively, you could measure the momentum transferred through the wave, and you'd get a certain result. Now aim the EM waves down a vertical shaft and measure them at some lower height, for example 10m or 100m lower. You'll get a higher frequency, and a higher momentum.
Well, why else would it be necessary to treat electron position probabilistically - if you didn't expect it to behave regularly in the first place?
Hm, we may have a different definition of "regular". Or rather, I'm not really sure what you mean by "regular". Could you explain?

Anyway, physicists use probability theory to model the electron position because it works. Perhaps one could say that they "deem it necessary to have the electron(s) of particular particle behaving in regular patterned ways" because that's what they see.
And nothing is interacting with the atom and its electron?
Nothing except the measurement device, which could be as simple as an EM wave (a photon). And that only because you can't even measure the position without having something interact with the electron.
I acquired a distaste for statistics from social science. I'm aware of the claimed benefits of statistical modeling. I dislike them because they substitute empirical realities with means. They promote forms of thinking that avoid exploring the full range of interactive possibilities between individuals. This could be true of humans or particles, I assume.
Ah, I see how you could come away that attitude :wink: I'm no expert on any social science, but as I understand it, what seems to happen a lot there is that you're working with data that is fundamentally qualitative, e.g. people's opinions. In order to apply math to social problems, you first have to quantify the system, i.e. come up with some way to use numbers to describe whatever you're studying, and inevitably a lot of useful and/or interesting information gets lost when you do that. You might get some interesting conclusion from a statistical analysis, but it's possible that that conclusion misrepresents the actual situation because of the way you chose to describe it numerically.

That's not the case in physics, though. In physics we deal with measurements and formulas, so everything is quantitative right from the start. So when you apply a statistical analysis, you don't lose information by converting things to numbers one way or another. For this reason, statistical results are a lot more reliable in physics than in pretty much any other science.

And anyway, the bottom line is, physicists have developed a system where you make predictions and test them using math (including statistics). It works really really well. So it doesn't seem that there's some empirical reality that's beyond the ability of math to describe, as there is in the social sciences.

[brainstorm]

I think you've moved from reasoning about the logic of the facts to simply recapitulating the facts as you know them. The topic of the OP is WHY light travels at the speed it does, not what the established facts of light behavior are.

Hm, we may have a different definition of "regular". Or rather, I'm not really sure what you mean by "regular". Could you explain?
Regular = the way you think about the Earth tracing the same orbital pattern each year with little if any deviation from last year's path. Physicists expected this from electron orbits in the Bohr model because of narrow assumptions about orbital motion, I think.

Anyway, physicists use probability theory to model the electron position because it works. Perhaps one could say that they "deem it necessary to have the electron(s) of particular particle behaving in regular patterned ways" because that's what they see.
Yes, it may also work to predict height by sex but that doesn't explain why a particular man or woman attained the height they did.

Nothing except the measurement device, which could be as simple as an EM wave (a photon). And that only because you can't even measure the position without having something interact with the electron.
Maybe not, but you could theorize it and theorize the potential effects and observe those.

Ah, I see how you could come away that attitude :wink: I'm no expert on any social science, but as I understand it, what seems to happen a lot there is that you're working with data that is fundamentally qualitative, e.g. people's opinions. In order to apply math to social problems, you first have to quantify the system, i.e. come up with some way to use numbers to describe whatever you're studying, and inevitably a lot of useful and/or interesting information gets lost when you do that. You might get some interesting conclusion from a statistical analysis, but it's possible that that conclusion misrepresents the actual situation because of the way you chose to describe it numerically.
And not only that, but you have created an individual picture from the average of a population of individuals. Thus when you look at causes and effects of particular aspects of the population, you tend to forget that the population doesn't actually exist as an entity but is purely an analytical construction.

That's not the case in physics, though. In physics we deal with measurements and formulas, so everything is quantitative right from the start. So when you apply a statistical analysis, you don't lose information by converting things to numbers one way or another. For this reason, statistical results are a lot more reliable in physics than in pretty much any other science.
That's exactly what social statisticians would claim about their methods vis-a-vis other methods.

And anyway, the bottom line is, physicists have developed a system where you make predictions and test them using math (including statistics). It works really really well. So it doesn't seem that there's some empirical reality that's beyond the ability of math to describe, as there is in the social sciences.
But statistics allows predictions about synthetic population means to be analyzed according to other means. Without a specific example, I couldn't show you the problem exactly, but if I could if I had all the details of the analysis in front of me.

[diazona]

I think you've moved from reasoning about the logic of the facts to simply recapitulating the facts as you know them. The topic of the OP is WHY light travels at the speed it does, not what the established facts of light behavior are.
Hey, I've been just stating the facts as I know them this whole time, in response to your questions and statements. (Except for the little bit I've said about how I don't think the fundamental nature of light speed can be described by physics, but that's speculative and is all I have to say on the topic)
Regular = the way you think about the Earth tracing the same orbital pattern each year with little if any deviation from last year's path. Physicists expected this from electron orbits in the Bohr model because of narrow assumptions about orbital motion, I think.
Aha. Physicists would know this as a periodic orbit. You're probably right about the assumptions - I guess they assumed this sort of behavior in the Bohr model (and the Rutherford model) because up until that point, the only sort of orbit anyone knew about was planetary orbits.
Maybe not, but you could theorize it and theorize the potential effects and observe those.
Well, theory predicts that you wouldn't measure anything without a measuring device :tongue2: Seriously though, in quantum mechanics you really have to take into account the effect of whatever you're using to do the measurement, since it influences the results. Quantum theory doesn't make predictions about what happens in the total absence of interactions.
And not only that, but you have created an individual picture from the average of a population of individuals. Thus when you look at causes and effects of particular aspects of the population, you tend to forget that the population doesn't actually exist as an entity but is purely an analytical construction.
Ah, I see. That's generally not a problem we have in physics. For instance, when physicists talk among each other about the radius of a hydrogen atom, they all know what they really mean is \sqrt{\langle\psi_{100}\rvert r^2 \lvert\psi_{100}\rangle} (the root mean square expectation value in the ground state), and that it's merely one statistic that characterizes a distribution, rather than The Radius.

However, we do often have that problem when trying to explain these things to people who haven't had it beaten into their heads by years of study :wink: in other words, non-physicists. When you say "radius of a hydrogen atom," someone who hasn't studied quantum mechanics might understandably think of it as a little solid sphere with that radius, and may not understand that there's a statistical distribution behind that. Or here's another one I've seen a couple times: when you talk about the half-life of some radioactive material, a layperson might think that all of the radioactive material will have disappeared after twice that time, and wouldn't understand that it's an exponential decay which never completely reaches zero.
That's exactly what social statisticians would claim about their methods vis-a-vis other methods.
Hmmm... well, that's a debate for another day.
But statistics allows predictions about synthetic population means to be analyzed according to other means. Without a specific example, I couldn't show you the problem exactly, but if I could if I had all the details of the analysis in front of me.
Well if you find a good example and are inclined to share, I'd be interested. (You meant an example from social science, not from physics, right?) Although perhaps it's best not to expand the scope of this discussion further than necessary :wink:

[JDługosz]

...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.

You would get inconsistent results for the resulting length, depending on how you measured the Second. I don't mean the number, which goes into the definition, but the resulting length that it spits out that should be a standard Meter. If you changed "something" in physics, perhaps a Second based on the fine structure constant (e.g. atomic clock) would come out the same, but a Second based on gravity or the strong force or the weak force (half-life of a neutron) would give a different interval of time and thus a different length.

We agree that if you changed everything, you've changed nothing. That means keeping all the unitless constants the same, not just one of them. They ultimately relate different aspects of physics, and every such relationship must be represented.

[JDługosz]

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.

I thought so. So if you measured the second using the Weak force, you would need to include that coupling constant as well, right? And to do so, you could observer something involving the Neutral Current (Z) reaction, or look at the statistical curve of neutron decay.

[JDługosz]

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

That's probably because you write in complete sentences with proper grammar and spelling, separate paragraphs, etc.; and each post shows interaction with the respondents (e.g. you took in and processed what was said).

I note this so people in "the other boat" might look at this thread as an example of how to do better.

[JDługosz]

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


As you can see worked out in Nothing but Relativity (http://arxiv.org/abs/physics/0302045) and other similar papers, you can start with the concepts of reciprocity and symmetry and work out the general form that the velocity addition must have in order to satisfy those constraints. What falls out is basically SR. The general form has a variable you can choose: negative doesn't work. Zero is no motion at all. Infinite is Newton's laws. And some positive number is SR. And, as the more philosophical posts here have been exploring, it doesn't matter what that number is as long as it's some positive and finite value. It just "is".

The ultimate speed "just is". What matters to you is how it compares to other things. And that says more about those other things than about light.

[jackmell]

Why not it's that fast simply because of the way the Universe was created? And if the Universe was created with different parameters, then the speed of light and other "constants" of nature would likewise be different. To me, that makes sense: nothing is constant. It all depends on which constructor was used for instantiation (what the parameters were when the Universe was created).

[mugaliens]

One of the things I learned a few years ago was how inextricably intertwined the speed of light happens to be with the Gravitational constant G, the Reduced Planck constat h-bar, the Coulomb constant ke, and Boltzmann's constant kB.

The relationships between these fundamental physical constants can be related by means of the Base Plank units (http://en.wikipedia.org/wiki/Planck_units)of length, mass, time, electric charge, and temperature. Furthermore, many other Derived Planck units eminate from the Base Planck units, all of which happen to coincide quite nicely with known and observed limits, both large and small, of our universe.

This is key, as by means of multiplication and division, many of the key equations found throughout all works of physics can be normalized.

In summary, all of physics hinges on the Base Planck units (http://en.wikipedia.org/wiki/Planck_units), including c. Thus, if you'd like to know more about why c is what it is, you need not study all of physics to appreciate the interrelationships. Instead, start by familiarizing yourself with Planck units (http://en.wikipedia.org/wiki/Planck_units)themselves.

Working through that entry help me tremendously towards understanding the bigger picture of how all of this fits together, as well as why c is c. It sure put a grin on my face! :)

[DaleSpam]

So if you measured the second using the Weak force, you would need to include that coupling constant as well, right?Yes, exactly.

[DaleSpam]

One of the things I learned a few years ago was how inextricably intertwined the speed of light happens to be with the Gravitational constant G, the Reduced Planck constat h-bar, the Coulomb constant ke, and Boltzmann's constant kB.Sure, that is because it is the dimensionless combinations of these constants that are actually physically meaningful.

[brainstorm]

Well if you find a good example and are inclined to share, I'd be interested. (You meant an example from social science, not from physics, right?) Although perhaps it's best not to expand the scope of this discussion further than necessary :wink:
Well, this should be another thread but there's no point because people will just post a bunch of reasons that statistics has good predictive ability. I notice examples of what I am saying in various scientific expressions all the time, but it's easier when they're directly on hand. A classical example would be Durkheim's study of suicide where he said that a group's suicide rate would be the propensity of any given individual to commit suicide. So, e.g. if he found 1% of Catholics committed suicide (made up number by the way), then he believed any given Catholic would have a 1% chance of becoming suicidal. It extrapolates generalizations from a model to individuals without considering the actual mechanical parameters influencing any single individual.

That's probably because you write in complete sentences with proper grammar and spelling, separate paragraphs, etc.; and each post shows interaction with the respondents (e.g. you took in and processed what was said).

I note this so people in "the other boat" might look at this thread as an example of how to do better.
I always do this, but maybe more explicitly in this thread. Glad to be used as a positive example for a change, though:)


One of the things I learned a few years ago was how inextricably intertwined the speed of light happens to be with the Gravitational constant G, the Reduced Planck constat h-bar, the Coulomb constant ke, and Boltzmann's constant kB.

The relationships between these fundamental physical constants can be related by means of the Base Plank units (http://en.wikipedia.org/wiki/Planck_units)of length, mass, time, electric charge, and temperature. Furthermore, many other Derived Planck units eminate from the Base Planck units, all of which happen to coincide quite nicely with known and observed limits, both large and small, of our universe.

This is key, as by means of multiplication and division, many of the key equations found throughout all works of physics can be normalized.

In summary, all of physics hinges on the Base Planck units (http://en.wikipedia.org/wiki/Planck_units), including c. Thus, if you'd like to know more about why c is what it is, you need not study all of physics to appreciate the interrelationships. Instead, start by familiarizing yourself with Planck units (http://en.wikipedia.org/wiki/Planck_units)themselves.

Working through that entry help me tremendously towards understanding the bigger picture of how all of this fits together, as well as why c is c. It sure put a grin on my face! :)
I would guess Planck units have something to do with why c is c. It's too bad you can't remember or say what you came up with. It would do a lot for the OP topic, I think.

Still, a mathematical relationship would not really satisfy me. I would like to see some qualitative reason why the speed of light relates to its momentum, for example, which I think would also have to entail some explanation for why a photon or EM wave carries the amount of energy it does. E.g. if a photon must be generated with a particular amount of energy because of its conditions of emission, then maybe it needs to travel at a particular speed to result in the correct amount of momentum in its moment of absorption when it reaches its destination.

[camel_jockey]

However, IMHO, the discussion you're interested in having is better had in philosophy than physics.

I have two points to make on this.

1) Firstly I agree that this is somewhat philosophical, and I love that! So interesting! Are there any other Lorentz scalars in any of our theories which describe motion with respect to time?

Unless there are such scalars, the speed of light is the only "speed-like" scalar to our knowledge and therefore must be the only fundamental, special, priviledged speed. We are then left with a situation where all other less fundamental speeds must be talked of in terms of the only special speed, the speed of light!

2) Therefore, c can be assigned any value. Preferably 1. Why it in this set of units carries no dimension, is yet to be understood by me! Is it just a way of saying "speed shows up more commonly than distance or time in our equations, so lets make speed the most fundemental of the three quantities and express the other two in terms of speed" ???

[brainstorm]

How would it change the question to ask what the speed of light is really dependent on and how? Is it, for example, always constant in a vacuum regardless of the level of gravitation? Does it even make sense to talk about light as having travel time? For example, when you hear that light takes 8 minutes to get from the sun to Earth, how can you say that there is something happening simultaneously on the sun and Earth that nevertheless takes 8 minutes to get from one to the other?

[DaleSpam]

2) Therefore, c can be assigned any value. Preferably 1. Why it in this set of units carries no dimension, is yet to be understood by me!I think you are referring to Geometrized Units where time is given dimensions of length meaning that speeds are dimensionless numbers (slopes):
http://en.wikipedia.org/wiki/Geometrized_unit_system

This is decidedly different from Planck Units where c is also numerically set to 1 but is still considered to have dimensions of L/T:
http://en.wikipedia.org/wiki/Planck_units

Afaik, the Planck units are much more widely accepted than geometrized units.

[brainstorm]

Could anyone answer the following question? It seems relevant to this thread to me for some reason:

If you took the amount of energy emitted as radiation by a particular electron's moment of momentum, and then applied that amount of energy to a free electron traveling through a vacuum, what velocity would the electron reach?

[pallidin]

Could anyone answer the following question? It seems relevant to this thread to me for some reason:

If you took the amount of energy emitted as radiation by a particular electron's moment of momentum, and then applied that amount of energy to a free electron traveling through a vacuum, what velocity would the electron reach?

I could be wrong, but I don't think a free electron "absorbs" photons.
Manipulated momentum through either an electric or magnetic field? Yes.

[diazona]

Regarding Durkheim's suicide study, that would make an interesting discussion. But this is not the place :wink:
Is it, for example, always constant in a vacuum regardless of the level of gravitation? Does it even make sense to talk about light as having travel time? For example, when you hear that light takes 8 minutes to get from the sun to Earth, how can you say that there is something happening simultaneously on the sun and Earth that nevertheless takes 8 minutes to get from one to the other?
Yes; yes, because light has a finite speed; what is it that is supposed to be simultaneous on the sun and the Earth? And who (what observer) is claiming that they are simultaneous?
If you took the amount of energy emitted as radiation by a particular electron's moment of momentum, and then applied that amount of energy to a free electron traveling through a vacuum, what velocity would the electron reach?
What do you mean "moment of momentum"?

I think it might be possible for a free electron to absorb a photon. You'd have to do a bit of math to see whether it's allowed by energy/momentum conservation. (I don't remember offhand for sure)

[brainstorm]

I'm not specifying that the free electron has to be propelled by a photon. What I'm trying to do is compare a given amount of energy in terms of how fast it causes a free electron to go. So let me be specific about the two quantities I want to compare:

1) The amount of momentum needed for a given orbital electron to generate a certain amount of light
2) The velocity attained by a free electron in a vacuum given the same amount of momentum from whatever source.

I guess what would be really interesting would be to plot one in terms of the other and look for a pattern, but I'm putting too much on my xmas list now. I'd like to just understand the relationship between quantities of radiation energy and electron velocity through a vacuum given the same amount of energy. Does this question make sense now?

[pallidin]

I think it might be possible for a free electron to absorb a photon. You'd have to do a bit of math to see whether it's allowed by energy/momentum conservation. (I don't remember offhand for sure)

Just as a suggestion: I think that question/answer needs to be firmly established before we can go responsibly further.
My own understating is that only "bound" electrons can "absorb" a photon, and that a free electron cannot. Again, I could be wrong.

[diazona]

I'm not specifying that the free electron has to be propelled by a photon. What I'm trying to do is compare a given amount of energy in terms of how fast it causes a free electron to go. So let me be specific about the two quantities I want to compare:

1) The amount of momentum needed for a given orbital electron to generate a certain amount of light
2) The velocity attained by a free electron in a vacuum given the same amount of momentum from whatever source.

I guess what would be really interesting would be to plot one in terms of the other and look for a pattern, but I'm putting too much on my xmas list now. I'd like to just understand the relationship between quantities of radiation energy and electron velocity through a vacuum given the same amount of energy. Does this question make sense now?
It makes a bit more sense, but it still needs to be clarified. Namely: by what physical process is the light produced? What do you mean by "amount" of light? What momentum specifically are you asking for? i.e. the momentum of what object? Before or after the production of the light? Or do you want a difference between two momenta?

The speed of an electron given a certain amount of momentum, assuming the electron started from rest, is given by solving the equation
p = \frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}
for v. I get
v = \frac{p}{\sqrt{m^2 + \frac{p^2}{c^2}}}
Just as a suggestion: I think that question/answer needs to be firmly established before we can go responsibly further.
My own understating is that only "bound" electrons can "absorb" a photon, and that a free electron cannot. Again, I could be wrong.
Actually I think you're right, since now I remember that the basic QED vertex (electron + photon → electron) is not a permitted physical process, due to momentum nonconservation. I guess I should do the math: let piμ be the initial 4-momentum of the electron, pfμ be its final 4-momentum, and qμ be the 4-momentum of the photon. Conservation states that
p_{i\mu} + q_{\mu} = p_{f\mu}
Squaring that:
p_i^2 + 2p_i\cdot q + q^2 = p_f^2
and since 4-momentum squared = ±mass squared (depending on metric),
±m_e^2 + 2p_i\cdot q + 0 = ±m_e^2
So this is only possible if p_i\cdot q = 0.
p_{i\mu} = (\gamma_i m c, \gamma_i m v \cos\theta_i, \gamma_i m v \sin\theta_i, 0)
q_{\mu} = (E/c, E/c, 0, 0)
so
p_i\cdot q = E\gamma_i m - E\gamma_i m \tfrac{v}{c}\cos\theta_i = E\gamma_i m\Bigl(1 - \tfrac{v}{c}\cos\theta_i\Bigr)
Since v/c < 1 and |cosθi| ≤ 1, this will never be equal to zero. Therefore a free electron can't absorb a photon without side effects.

If I messed something up there, please do point it out.

[brainstorm]

It makes a bit more sense, but it still needs to be clarified. Namely: by what physical process is the light produced? What do you mean by "amount" of light? What momentum specifically are you asking for? i.e. the momentum of what object? Before or after the production of the light? Or do you want a difference between two momenta?

Your equation conversions seem complicated. I'm sorry I can't appreciate them more with my skill level. The momentum I'm thinking of, I guess, is maybe the amount that goes into bumping the electron to get it to produce the photon. So, let's say you can come up with the acceleration of an electron that results in a certain amount of radiation-emission. I guess I would like to know how much energy the electron gained and how much it lost to generate the given photon. Then I would want to know how fast an electron would travel if it was given that amount of energy as straight-line momentum in a vacuum.

Honestly, I'm embarrassed here because I'm getting lost in what I want to know. Basically, I want to compare electron-velocity with radiation-wavelength for a given amount of energy.

Maybe a better question to ask would be how long is the radiation beam emitted with one Planck unit of energy (is this the unit that is supposed to be the absolute smallest amount of energy that can be carried by an EM wave at a given frequency?)

[samuelwang]

I dont know a lot about the relativity theories yet, but here is my interpretation about this phenomena. I remember someone told me that gravity has effect on the time, and somehow I think the speed of light is relate to time, so may be this constant is a consequence as an equilibrium of all the gravity in this universe, may be?

[diazona]

Your equation conversions seem complicated. I'm sorry I can't appreciate them more with my skill level. The momentum I'm thinking of, I guess, is maybe the amount that goes into bumping the electron to get it to produce the photon. So, let's say you can come up with the acceleration of an electron that results in a certain amount of radiation-emission. I guess I would like to know how much energy the electron gained and how much it lost to generate the given photon. Then I would want to know how fast an electron would travel if it was given that amount of energy as straight-line momentum in a vacuum.
Sorry, still not clear. I think it'd be really important to specify what physical process is producing the photon, e.g. an atomic energy level transition, brehmsstrahlung ("braking radiation," produced when an electron is decelerated by electrical interactions), synchrotron radiation, etc. Once you figure that out, you can talk about what momentum/energy/whatever you're looking for, and what additional information you might need to figure it out.
Honestly, I'm embarrassed here because I'm getting lost in what I want to know. Basically, I want to compare electron-velocity with radiation-wavelength for a given amount of energy.
That's a little clearer. To be precise, you can calculate these two quantities:
The speed of an electron which has an amount of kinetic energy E is
v = c\sqrt{1 - \biggl(\frac{mc^2}{E + mc^2}\biggr)}
The wavelength of a photon (quantum of EM radiation) with energy E is
\lambda = \frac{hc}{E}
In both equations c is the speed of light and h is Planck's constant. m is the mass of the electron.
Maybe a better question to ask would be how long is the radiation beam emitted with one Planck unit of energy (is this the unit that is supposed to be the absolute smallest amount of energy that can be carried by an EM wave at a given frequency?)
"Planck unit of energy" is something different, but I get your meaning. Assuming that by "how long" you mean the wavelength, that is. If you have a radiation "beam" at a given frequency f, and that beam contains the minimum possible energy it can have with that frequency, its energy will be E = hf and its wavelength will be given by the formula I wrote above, λ = hc/E.

[granpa]

the speed of the electron in the bohr atom divided by the speed of light is equal to α

1/137

[pongo38]

Can someone tell me, concerning the speed of light, what is the reference frame for that? The cosmologists talk about 'so many light years' distance to another object in the sky. Is the solar system the frame of reference. or the galaxy, or some invariant arrangement of stars out there?

[brainstorm]

Sorry, still not clear. I think it'd be really important to specify what physical process is producing the photon, e.g. an atomic energy level transition, brehmsstrahlung ("braking radiation," produced when an electron is decelerated by electrical interactions), synchrotron radiation, etc. Once you figure that out, you can talk about what momentum/energy/whatever you're looking for, and what additional information you might need to figure it out.

I never saw this post until now. Are these all different processes where electrons generate photons? I only knew on a general level that electrons could jump up and down an orbit to generate a photon and the braking energy sounds like an idea I once had about why electric current jumping across a short circuit or static electricity generates a spark. Am I talking about anything close to these?

I don't really know what to do with the equations you provided, but thanks for trying. I wonder if the wavelength of light has anything to do with the acceleration and deceleration of the electron. In other words, could it be as simple as an electron working like a speaker that pulsates to send out a sound wave, where I assume the frequency of the sound wave is caused by how far and fast the speaker moves forward and back? I guess even if that were the case, though, the speed of the wave could be as fast or slow as the medium allows and transfer the same energy. The problem of a medium for light always seems to creep up somehow.

[JDługosz]

could it be as simple as an electron working like a speaker that pulsates to send out a sound wave, where I assume the frequency of the sound wave is caused by how far and fast the speaker moves forward and back?

It's not like that at all. In some sense it's "simple as" that, though. Try reading Feynman's little book "QED". It's very approachable and explains everything.

[Ash Small]

The simple answer here is that the speed of light, c, is equal to the square root of 'energy divided by mass'.

Einstein said this a hundred years ago.

I think the question we should be answering is " why is it the 'square root' of energy divided by mass?".

Either that or "Why is the maximum energy mass can have a finite number?" ie "Why can't a mass have infinite energy?"

[brainstorm]

The simple answer here is that the speed of light, c, is equal to the square root of 'energy divided by mass'.
Wouldn't this mean that E=(MC)^2 instead of E=MC^2 ?

I think the question we should be answering is " why is it the 'square root' of energy divided by mass?".
Isn't that basically what the OP was asking? I.e. what is the relationship between inertia-gravity relations and mass-energy relations?

Either that or "Why is the maximum energy mass can have a finite number?" ie "Why can't a mass have infinite energy?"
Are you referring to kinetic energy of an object in motion, i.e. momentum? Or the energy constituting the particle internally? Or both?

[Ash Small]

Wouldn't this mean that E=(MC)^2 instead of E=MC^2 ??




I don't think so. If E/M=c^2 then Sqr Root of (E/m)=c.


Isn't that basically what the OP was asking? I.e. what is the relationship between inertia-gravity relations and mass-energy relations??




Yes. I've just re-phrased the question. Surely this is the reason why speed of light in a vacuum is constant?

Are you referring to kinetic energy of an object in motion, i.e. momentum? Or the energy constituting the particle internally? Or both?

The energy constituting the particle internally.

Surely in order to understand why c is a constant we need to explain the relationship between E and M?

[ZapperZ]

I don't think so. If E/M=c^2 then Sqr Root of (E/m)=c.







Yes. I've just re-phrased the question. Surely this is the reason why speed of light in a vacuum is constant?



The energy constituting the particle internally.

Surely in order to understand why c is a constant we need to explain the relationship between E and M?

OK, this is getting to be a bit ridiculous.

If you think that having an expression to relate these things is fundamental and definitive, then you will have a lot of issues to deal with when I pull out another expression, such as:

\alpha=\frac{e^2}{\hbar c}

I will even argue that, unlike E=mc^2, the expression above is more fundamental because it contains only fundamental constants, and the relationship produced a dimensionless number of the fine structure constant \alpha! So how about them apples?

One needs to be VERY careful when one is playing around with equations, and the making such remarks that it has significantly deep enough meaning without understanding the physics, and without understanding other aspects of physics. To make such claim that the relationship between E and M is the actual CAUSE of the constant c is speculative overreaching at best!

Zz.

[brainstorm]

To make such claim that the relationship between E and M is the actual CAUSE of the constant c is speculative overreaching at best!


E and M are the only variables, right? There's no medium that would determine the speed of light, right? So what else could be responsible for the speed of light constant C except some fixed relationship between the two variables?

[Raphie]

Wouldn't this mean that E=(MC)^2 instead of E=MC^2 ?

Energy is expressed in Joules, mass in kilograms and light in meters/second. Thus c^2 --> meters^2/sec^2 and mc^2 = kilograms^1 * meters^2/sec^2.

The units for Joules are: kilograms^1 * meters^2/sec^2. Therefore...

kilograms^1 * meters^2/sec^2 = kilograms^1 * meters^2/sec^2

The units for (MC)^2 could be expressed as: Joule-kilogram (i.e. E*kilogram), as opposed, for instance, to Joule-second, which is the unit expression for Planck's Constant. So, in short, no, E does not equal (MC)^2.

[ZapperZ]

E and M are the only variables, right? There's no medium that would determine the speed of light, right? So what else could be responsible for the speed of light constant C except some fixed relationship between the two variables?

But you are making a faulty assumption that THAT is the only valid equation to consider. I've given you one other. So which one do you choose? It appears that you simply chose one and ignored the rest of the equations in physics to make your deduction about the "cause" of the speed of light. This is puzzling logic.

Zz.

[Ash Small]

But you are making a faulty assumption that THAT is the only valid equation to consider. I've given you one other. So which one do you choose? It appears that you simply chose one and ignored the rest of the equations in physics to make your deduction about the "cause" of the speed of light. This is puzzling logic.

Zz.

Zapper, I chose a reasonably simple equation without any dimensionless constants for a very good reason. I'm aware that there are other equations with c in them, but E=Mc^2 was the simplest one I could think of.

I assumed it would be easier for most readers of this thread to relate to, rather than more complex equations, for example, ones including the reduced plank's constant and alpha.

I was trying to keep it simple, and to make a point at the same time.

I wasn't suggesting that the relationship between E and M was the 'cause' of the speed of light, but that the 'cause' of the speed of light is also related to the 'reason' why the relationship between E and M is what it is.

If we can explain WHY the relationship between E and M is a constant, ie c^2, then maybe this will help us understand why the speed of light in a vacuum is what it is.

Raphie, I haven't said E=(Mc)^2, you've not followed the maths.

[NetMage]

Well, my personal opinion is: If the universe is expanding, yet nothing travels faster than light ( to our knowledge ), then the universe is expanding at <= c. Thus this changes the fundamental question to: "why does nothing travel faster than c". And that is a philosophical question. :)

[ZapperZ]

Zapper, I chose a reasonably simple equation without any dimensionless constants for a very good reason. I'm aware that there are other equations with c in them, but E=Mc^2 was the simplest one I could think of.

So just using the "simplest" equation as the criteria, you propose to use that equation as the foundation for explaining the speed of light? That's it? And you think this is a legitimate criteria without making any consideration to the actual physics? You are comfortable with doing that?

This is getting to be a bit silly. You are saying that just because F=ma is "simple", then m is "caused" by F and a, regardless of the fact that if F=a=0, m is undefined! So an object not acted upon by any force as an undefined mass! All this nonsense is obtained using your principle of using the simplest equation and then deriving profound meaning out of it as containing the "cause" of it. This makes sense to you? If not, apply the same thing to E=mc^2 to massless particles (photons) and see if you think this causes "c".

You are confusing the ability to make QUANTITATIVE measurement of something with the "cause" of something. Nothing in E=mc^2 indicates that E and m are the "cause" of the constant speed of light. Unless you think Einstein is utterly dumb, then you have to argue why HE, of all people, never made such a connection, and physics continues to consider that the constancy of the speed of light is a POSTULATE of Special Relativity.

Zz.

[D H]

Well, my personal opinion is: If the universe is expanding, yet nothing travels faster than light ( to our knowledge ), then the universe is expanding at <= c.
The expansion rate of the universe is not a velocity; it doesn't even have units of velocity. Even if it did have units of velocity, that still would not mean that the expansion rate is constrained by the speed of light.

[Ash Small]

So just using the "simplest" equation as the criteria, you propose to use that equation as the foundation for explaining the speed of light? That's it? And you think this is a legitimate criteria without making any consideration to the actual physics? You are comfortable with doing that?

This is getting to be a bit silly. You are saying that just because F=ma is "simple", then m is "caused" by F and a, regardless of the fact that if F=a=0, m is undefined! So an object not acted upon by any force as an undefined mass! All this nonsense is obtained using your principle of using the simplest equation and then deriving profound meaning out of it as containing the "cause" of it. This makes sense to you? If not, apply the same thing to E=mc^2 to massless particles (photons) and see if you think this causes "c".

You are confusing the ability to make QUANTITATIVE measurement of something with the "cause" of something. Nothing in E=mc^2 indicates that E and m are the "cause" of the constant speed of light. Unless you think Einstein is utterly dumb, then you have to argue why HE, of all people, never made such a connection, and physics continues to consider that the constancy of the speed of light is a POSTULATE of Special Relativity.

Zz.

No, Zapper, you've misunderstood.

I've just re-pr=hrased the question, not provided an answer.

There are other ways to re-phrase the question as well, as you have pointed out.

(by the way, photons are energy, they have no mass, but they do travel at the speed of light.If you want me to put this mathematically, E/c^2=0)

[Driftwood1]

The expansion rate of the universe is not a velocity; it doesn't even have units of velocity.

The boundary of an FINITE universe can be expanding and expressed in terms of a velocity.

You could also express it as a change in volume per time. Its a rate so time must be there - there are a few different quantities you can use on top of time

[ZapperZ]

No, Zapper, you've misunderstood.

I've just re-pr=hrased the question, not provided an answer.

Really? Let's review, shall we?

Yes. I've just re-phrased the question. Surely this is the reason why speed of light in a vacuum is constant?
The energy constituting the particle internally.

Surely in order to understand why c is a constant we need to explain the relationship between E and M?

You've just claimed that the relationship between E and M is the reason why the speed of light is a constant in vacuum. Where did I misunderstood you here?

(by the way, photons are energy, they have no mass, but they do travel at the speed of light.If you want me to put this mathematically, E/c^2=0)

This is nonsense. E is not zero for a photon, and c isn't zero for a photon. How in the world were you able to convince yourself that non-zero/non-zero = 0? What kind of math are you using?

I think you still have a lot to learn about basic physics before making such outlandish speculation.

Zz.

[D H]

The boundary of an FINITE universe can be expanding and expressed in terms of a velocity.
Assuming a finite universe, yes you could express the expansion of the universe in terms of a velocity. The diameter, for example. The speed of light would not be a constraint on that velocity.

[Raphie]

(by the way, photons are energy, they have no mass, but they do travel at the speed of light.If you want me to put this mathematically, E/c^2=0)

Ash Small, whether correct or incorrect, is this the logic you were getting at?

A) If mass of photon = 0, then e=mc^2 = e = 0*c^2
B) Anything multiplied by 0 = 0, therefore e = 0 for energy of photon
C) If E = MC^2, then by substitution e = mc^2, therefore 0 = 0*c^2
D) By rearrangement of terms, 0/c^2 = 0

If the energy of a photon is not 0 Joules, but its mass is 0 kilograms, then there does seem to be a contradiction here, not a flaw in your ability to perform basic mathematics. Two obvious "kludges" to reconcile that contradiction, it seems to me, again whether wrong or right, is to assume either 1) that photon mass is not equal to 0, or b) that the M term should be considered in terms of n!/|n-1|!

1) That a photon has mass, however small, has been considered by physicists and is an issue of open debate.
2) The factorial argument is no more than a mathematically, but not physically, valid "workaround" to handle 0 that leaves one with the following logical (in isolation), but absurd (not in isolation), statement:

A) If mass of photon = 0, then e=mc^2 = e = (0!/|0-1|!) kg.*c^2 = c^2
B) "Anything" multiplied by 1 = "Anything", therefore, e = c^2 for energy of photon
C) If E = MC^2, then by substitution e = 1 kg. *c^2 = mc^2
D) By rearrangement of terms, e/c^2 = 1 kg.
Which is absurd because it suggests that the mass of a photon and the mass of 1 kilogram are equivalencies in terms of total energies...

To ZapperZ et al.: What do the physicists have to say regarding energy of a photon beyond, for instance:

The minimum energy required to eject an electron from the surface is called the photoelectric work function. The threshold for this element corresponds to a wavelength of 683 nm. Using this wavelength in the Planck relationship gives a photon energy of 1.82 eV.
http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html

A) Is photon mass 0 or not 0?
B.i) If not 0, then why do text books repeatedly propagate this meme?
B.ii) If actually 0, then why do physicists repeatedly tell those who point out the contradiction that Ash Small has pointed out that it is their logic, basic ability to perform mathematics, and/or knowledge of physics that is faulty rather than the equations they are relying upon?

Best,
Raphie

P.S. I don't mean this post in a confrontational way, and, straight-up, I am not contending that the energy of a photon is either 0 or c^2 Joules, but I do desire to defend Ash Small's basic reasoning capabilities here. Any reasonable person following the logic through, using not "made-up" math, but elementary algebra, might well ask similar questions. Intended as a response to:

This is nonsense. E is not zero for a photon, and c isn't zero for a photon. How in the world were you able to convince yourself that non-zero/non-zero = 0? What kind of math are you using?

I think you still have a lot to learn about basic physics before making such outlandish speculation.

[ZapperZ]

To ZapperZ et al.: What do the physicists have to say regarding energy of a photon beyond, for instance:

The minimum energy required to eject an electron from the surface is called the photoelectric work function. The threshold for this element corresponds to a wavelength of 683 nm. Using this wavelength in the Planck relationship gives a photon energy of 1.82 eV.
http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html

A) Is photon mass 0 or not 0?
B.i) If not 0, then why do text books repeatedly propagate this meme?
B.ii) If actually 0, then why do physicists repeatedly tell those who point out the contradiction that Ash Small has pointed out that it is their logic, basic ability to perform mathematics, and/or knowledge of physics that is faulty rather than the equations they are relying upon?

Best,
Raphie

P.S. I don't mean this post in a confrontational way, and, straight-up, I am not contending that the energy of a photon is either 0 or c^2 Joules, but I do desire to defend Ash Small's basic reasoning capabilities here. Any reasonable person following the logic through, using not "made-up" math, but elementary algebra, might well ask similar questions. Intended as a response to:

Please read the FAQ in the General Physics forum.

Zz.

[Ash Small]

Really? Let's review, shall we?



You've just claimed that the relationship between E and M is the reason why the speed of light is a constant in vacuum. Where did I misunderstood you here?



This is nonsense. E is not zero for a photon, and c isn't zero for a photon. How in the world were you able to convince yourself that non-zero/non-zero = 0? What kind of math are you using?

I think you still have a lot to learn about basic physics before making such outlandish speculation.

Zz.

Zapper, Einstein said his theories were only approximations. I seem to remember this is why he gave us general relativity and special relativity.

a very small number (~0),divided by a very large number (~infinity) equals approximately zero.

I think you'll find that a lot of Einstein's equations worked like this.

(I admit that the other point you raised wasn't worded very well. The reason why E/M=c^2 is the same as (or related to) the reason why the speed of light is a constant, I accept that I didn't phrase it well. I was trying to make a point as simply as possible.)

[D H]

Ash Small, whether correct or incorrect, is this the logic you were getting at?

A) If mass of photon = 0, then e=mc^2 = e = 0*c^2
B) Anything multiplied by 0 = 0, therefore e = 0 for energy of photon
C) If E = MC^2, then by substitution e = mc^2, therefore 0 = 0*c^2
D) By rearrangement of terms, 0/c^2 = 0

If the energy of a photon is not 0 Joules, but its mass is 0 kilograms, then there does seem to be a contradiction here, not a flaw in your ability to perform basic mathematics.
The only flaw is using the wrong equation. The correct equation is

E^2 = (m_0c^2)^2 + p^2c^2

from which it should be clear that a particle with zero mass but non-zero momentum will have non-zero energy.


1) That a photon has mass, however small, has been considered by physicists and is an issue of open debate.
There is no contention amongst physicists that the photon has zero mass. None. Experimental physicists have attempted to measure the photon's rest mass because one of the main jobs of experimentalists is to verify the assumptions and predictions of theoreticians. Experimentalists don't believe anything told to them by theoreticians unless they see first-hand evidence in their experiments that the theoreticians got it right this time. That certainly is the case here. Every experimental attempt to measure the rest mass of the photon has come up with zero, to within experimental error.

2) The factorial argument is no more than a mathematically, but not physically, valid "workaround" to handle 0 that leaves one with the following logical (in isolation), but absurd (not in isolation), statement: ...
What factorial argument?

Your entire post is based on extrapolations from the overly simplistic E=mc2.

[ZapperZ]

Zapper, Einstein said his theories were only approximations. I seem to remember this is why he gave us general relativity and special relativity.

a very small number (~0),divided by a very large number (~infinity) equals approximately zero.

What does this have anything to do with that you did? You were dividing 0 with 0!

I think you'll find that a lot of Einstein's equations worked like this.

(I admit that the other point you raised wasn't worded very well. The reason why E/M=c^2 is the same as (or related to) the reason why the speed of light is a constant, I accept that I didn't phrase it well. I was trying to make a point as simply as possible.)

Er.. I don't think you know Einstein very well, or for that matter, understand what is meant by "theory".

There has been a lot of nonsense posted in this thread.

Zz.

[Raphie]

@ZapperZ: Thank you for the FAQ reference.

@DH:
Your entire post is based on extrapolations from the overly simplistic E=mc2.

You are correct. And that is exactly my point. e=mc^2 is what most regular people (the layman) are taught. I am saying they are taught wrong (or rather, over-simplistically) and therefore extrapolate incorrectly.

As such, I was not arguing that a photon has no energy, nor that a photon has mass, but that such suppositions follow from e=mc^2 using elementary algebra. As far as that goes, thank you for including the correct equation in your response. It's very helpful in regards to my personal understanding and hopefully to other's as well.

As for the issue of a photon having mass or no, I fully understand that the general consensus is definitely "no," but I also know that this question has been debated over and over again (although it would seem I overestimated the seriousness with which that debate is viewed...) and I also know that photons can be considered to have mass in a "relativistic sense," unless I am being "taught wrong" by Steven S. Zumdahl.

Chemical principles, Page 528 by Steven S. Zumdahl
"A photon has mass only in a relativistic sense -- it has no rest mass"

Best,
Raphie

[Ash Small]

What does this have anything to do with that you did? You were dividing 0 with 0!.

Zapper, I was actually dividing E by c^2 (within the context of E=Mc^2, which we all know is flawed)

In this case, E is a very small number and c^2 is a very large number, so the answer is ~0.

On the subject of dividing 0 by 0, however, zero divided by anything is zero, and anything divided by zero is infinity, however, in this case, zero is nothing, not 'anything', so I assume that this follows the case where anything divided by itself is one. (0/0=1). I'm not sure of this, just doing my best to answer your question.

[ZapperZ]

Zapper, I was actually dividing E by c^2 (within the context of E=Mc^2, which we all know is flawed)

In this case, E is a very small number and c^2 is a very large number, so the answer is ~0.

This is wrong. What makes you think "E" is always "very small number"? For example, what is E for an electron? Do you get this to be "~0" as well?

On the subject of dividing 0 by 0, however, zero divided by anything is zero, and anything divided by zero is infinity, however, in this case, zero is nothing, not 'anything', so I assume that this follows the case where anything divided by itself is one. (0/0=1). I'm not sure of this, just doing my best to answer your question.

You need to learn calculus, especially complex algebra. What you said here is mathematically incorrect.

In case this is something you don't realize already, this forum is populated with professional physics, mathematicians, engineers, etc. Considering that from my perspective, you are barely understanding basic physics, I would strongly suggest that you do not take it upon yourself to try and "teach" basic physics and math on here, something which I don't think you understand already.

If the OP has further questions, please contact me. If not, this thread is done.

Zz.