# Why does light travel at the speed it does?

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".

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

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
Staff Emeritus
Gold Member
kenimpzoom said:
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
Welcome 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.

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

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).)

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

Yep, you get it!

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?

Dale
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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
Homework Helper
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.

Dale
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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
Mentor
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.

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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?

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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".

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.

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.

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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.

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
Gold Member
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
Gold Member
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).

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

Dale
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2021 Award
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:

https://www.physicsforums.com/showpost.php?p=2011753&postcount=55
https://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
Homework Helper
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:

https://www.physicsforums.com/showpost.php?p=2011753&postcount=55
https://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

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.

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Dale
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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.

Dale
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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.

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

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.

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Dale
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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.

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.