Why Does C Have a Particular Value, and Can It Change? - Comments

[bcrowell]

bcrowell submitted a new PF Insights post

Why Does C Have a Particular Value, and Can It Change?

Continue reading the Original PF Insights Post.

 

[HomogenousCow]

What is the difference between a constant which can be "made unitless" like c and h-bar, and units which are "inherently unitless" such as the fine structure constant?
It's always bothered me that we can just measure time in units of length due to c. I get that since c is universal we can naturally relate one arbitrary unit of distance to a unit of time, however it doesn't seem immediately obvious to me that this warrants equating the two quantities.

 

[PAllen]

What is the difference between a constant which can be "made unitless" like c and h-bar, and units which are "inherently unitless" such as the fine structure constant?
It's always bothered me that we can just measure time in units of length due to c. I get that since c is universal we can naturally relate one arbitrary unit of distance to a unit of time, however it doesn't seem immediately obvious to me that this warrants equating the two quantities.

The process of making c unitless is equivalent to the process of selecting an inherently unitless constant. Both entail the feature that you lose the ability to state whether a change in the unitless value is attributable to a change in a particular constant with dimensions.

 

[Skilroyishere]

No. C is constant. The variable lies in the conditions in which this standard is influenced. All the constants that we have established to this point are based on our unique (base) perspective. The reality of the physical properties that we observe and postulate are slightly skewed. Accepting the fact that all constants are subject to the effects of the properties and/or restrictions of any environmental variables that may alter that constant. We now understand that the constant is not our own perspective. The constant that exists is with out. The constant is 0. A very cold 0, It has no variables. Our perspective tells us the symbol g has relative standard. The numerical value for the acceleration of gravity, most accurately known as 9.8 m/s/s. This also is subject to the variables of a its surroundings. Now that we have established that all constants are measurable by: wave, speed, density, strength, length, resonance or all of the above.
A constant does not mean it cannot change. It simply means it is a scale to measure inconsistencies.

 

[harrylin]

It appears to me to be the wrong answer to a slightly ambiguously or imprecisely asked question... People asking such a question are not likely to care if c is expressed in m/s, miles/h or "natural" units.

 

[Dale]

This is really going off topic. Let's keep further discussion focused on the speed of light or the fine structure constant and not a referendum on GR or dark matter.

 

[Vanadium 50]

Let me tell you why I find the Webb result unconvincing.

• It's Webb. Whenever there is a positive effect, it seems that his name is there. That doesn't mean I would never believe anything he said, but it does mean that I consider his track record when evaluating his results? Is this scientific? Who knows - but it is nevertheless a good idea.
• The statistics are not convincing. There are a few hundred possible directions in the sky the dipole might be pointing. But when this is considered it doesn't change the p-value by a factor of 100. It changes it by less than a factor of 2. What I would have liked to see is a test where the sources are placed randomly on the sky many times, and the fraction of times a random placement is at least this significant reported.
• There are even more significant results that I am unconvinced by. DAMA/LIBRA has a 9 sigma signal with 7 cycles. I am absolutely convinced they see a modulation. I, like much of the community, is unconvinced that dark matter is responsible.
• At 10^-5 (their reported signal) all sorts of systematics start showing up. For example, with room-temperature spectroscopy, that's where thermal expansion of your instrument starts to limit you. At that level, I'd want to see not just analysis of data, but contributions from the people who built and operate the instrument, explaining how they have addressed this.

 

[Murdstone]

Everyone seems far adrift from the original question of the OP.
Why Does C Have a Particular Value, and Can It Change?

C has a finite value. It is fast but not amazingly fast. What constrains C to have the value that it has? The value of C is not arbitrary. - Why Does C Have a Particular Value?

c=f(xi) i =1,2,...n Where xi is a constraint on the value of c. Can It Change? If you could change the value of one of the constraints then you should be able to change the value of c. For a constant c the implication is the constraints are also constant.

Unfortunately, to date, we do not know what constrains c. We can measure c but know little else about how this value is coming about.

This relates to Newton's gravity. Gravity was assumed and all that was actually done was measure its effects.

 

[vanhees71]

There's not so much more to say about this issue. It's a fundamental law that spacetime is best described by relativistic spacetime continua of nature. It's a very well established basic empirical fact. In this sense you can set ##c=1## and measure spatial distances and temporal durations in the same unit. In principle that's what's realized in the SI of units, because ##c## has a fixed value and is just a conversion between distance and time units in order to have convenient numbers in everyday life. The choice of this value is arbitrary and was done in a way to reproduce the previously defined units of length, metre, and time, second.

 

[Dale]

What constrains C to have the value that it has? The value of C is not arbitrary. - Why Does C Have a Particular Value?

c=f(xi) i =1,2,...n Where xi is a constraint on the value of c. Can It Change? If you could change the value of one of the constraints then you should be able to change the value of c. For a constant c the implication is the constraints are also constant.

Unfortunately, to date, we do not know what constrains c.

We know exactly what constrains c to have the value that it has: our choice of units. The value of c can change if we change our units. Because we can change it by changing our units we often use units where c=1.

You probably mean the fine structure constant, not c.

 

[Murdstone]

Sure you can alter the value of c by changing the units of measurement. However, once your choice of units has been determined the question is why does it take on the value that it does.

e.g. - c = 186,000 mi/sec Why is c not more or less than this value.

 

[Dale]

Sure you can alter the value of c by changing the units of measurement. However, once your choice of units has been determined the question is why does it take on the value that it does.

Because of your choice of units. There is no additional explanation needed or possible. The choice of units wholly accounts for the value of C.

e.g. - c = 186,000 mi/sec Why is c not more or less than this value.

c is 186000 mi/s because of the length you chose to call 1 mi and the duration you chose to call 1 s.

Again, if you dig down to the question that you probably actually want to know, it is most likely a question about the fine structure constant.

 

[Nugatory]

e.g. - c = 186,000 mi/sec Why is c not more or less than this value.

When you use the laws of electricity and magnetism to calculate (as Maxwell first did in 1861) the speed at which electromagnetic radiation propagates through a vacuum, that's the value you get.

Of course you could ask why the laws of E&M are what they are and not something else... but if we answered that question, the answer would just lead to another "Why?" question, and the regress will never end.

As DaleSpam as pointed out, the essential fact about the laws of E&M that lead to the speed of light being what it is is the value of the fine structure constant - and that's a experimental fact about the universe we live in.

 

[bcrowell]

When you use the laws of electricity and magnetism to calculate (as Maxwell first did in 1861) the speed at which electromagnetic radiation propagates through a vacuum, that's the value you get.

I disagree both with the factuality and the spirit of this statement.

First off, this simply incorrect. If you write Maxwell's equations in a sensible system of units where c=1, they predict that light travels at speed 1. Maxwell's equations are not predicting anything about the speed of light that you didn't put in by hand. The fact that the value of c was put in by hand just happens to be obscured by one of the common ways of writing them, with epsilon-noughts and mu-noughts.

Second, this statement makes it sound as though c was defined as the speed of light. It's not. So appealing to Maxwell's equations to explain c is backwards.

Of course you could ask why the laws of E&M are what they are and not something else... but if we answered that question, the answer would just lead to another "Why?" question, and the regress will never end.

Not true. We understand quite well, based on more fundamental considerations, why Maxwell's equations predict that light travels at the universal speed c. They predict it because light is massless, and SR says that massless things travel at c. Furthermore, we understand quite well, based on more fundamental considerations, why there is a universal speed c in SR: https://www.physicsforums.com/threa...-in-all-reference-frames.445032/#post-2970609

DaleSpam's explanation is both necessary and sufficient: c has the numerical value it does in a particular system of units simply because we chose that system of units.

 

[vanhees71]

Well, it's not that wrong to cite Maxwell in connection with the speed of light, ##c##. In his time the electromagnetic units were similar to what we call Gaussian units nowadays:

https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_unitshttps://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units

When Maxwell added his famous "displacement current" to the Ampere Law, he realized that this implies the existence of electromagnetic waves, which propagate with the speed of light, ##c##, which brought him to the conclusion that light might in fact be electromagnetic waves, i.e., he did not only unify electricity and magnetism (as well as the local conservation law for the electric charge) into a consistent system of equation but also incorporated optics, the theory of light, into electromagnetism. The direct proof that electromagnetic really exist came then with the famous experiments by H. Hertz in the physics lecture hall in Karlsruhe, where he could do his experiments only in the semester break in order not to disturb the ongoing lectures ;-)).

Of course again, this history underlines what was said numerous times in this thread: The numerical value of ##c## is arbitrary. From the point of view of relativity, which of course has also been discovered by the careful analysis of the Maxwell equations and experiments concerning the question, whether there exists a preferred inertial reference frame (the "aether rest frame"), there's no reason to invent different units for length and time intervals. The most natural system of units occurs, when you put all the fundamental natural constants to 1.

Taking only mechanics and electromagnetism the only fundamental constant is the speed of light. Setting this to 1 and using some arbitrary unit for distances or times and masses, you have already one base unit less than in the CGS system, and you measure space and time intervals in the same unit of length (e.g., light seconds).

Considering also quantum theory, one more fundamental constant enters, Planck's modified action, ##\hbar##. Setting this also to 1 you have again one base unit less. You can just measure masses (and also energies and momenta) in terms of the inverse length unit. Rationalizing the Maxwell equations and using this units leads to the natural units used in high-energy particle (HEP) physics. Now we have only one base unit left, the length unit (in HEP usually ##1 \text{fermi}=1 \text{femto metre}=1 \text{fm}=10^{-15} \mathrm{m}##. All the fundamental constants of the standard model are then dimensionless couplings (for the strong, the weak, and the electromagnetic interaction, and the Yukawa couplings of the quarks and leptons to the Higgs field), and a mass scale (or the vev of the Higgs boson).

Finally, also considering gravitation and General Relativity, you have one more fundamental dimensionful unit left, Newton's coupling constant of gravity. This can be used to eliminate the last remaining base unit, and you are working in fundamental Planck units. All quantities are then given in dimensionless numbers.

In fact, what's done in an international effort concerning the SI is to do exactly such a program. One tries to trace back the values of all the base units of the SI to the fundamental constants of nature. This has been already done for space-time units by defining the speed of light to a certain value and define the unit of length via the very accurately representable unit of time (the second) and this value of the speed of light.

I guess, it won't take too long, until the unit of mass, kg, is redefined in the one or the other way: either one uses the "Watt balance" and fixes Planck's constant in terms of the SI units or by defining Avogadro's constant and the atomic weight of a certain isotope-clean element (most probably silicon-28).

https://en.wikipedia.org/wiki/Kilogram

 

[Dutchr]

The speed of light is a constant because we measure time and distance in the same way.

Distance is best measured by calculating how far a light ray travels in a unit of time. This is exactly how the meter is defined in physics. Time is best measured by calculating how many back and forth vibrations light/fundamental forces do through a distance in some fundamental clock (vibrations of a Cesium atom for example). To the fundamental forces and to the fields that make up everything time and distance are measured in a very similar way. See the fundamental problem?

Could the speed of light even change from an observer's perspective if say its value were cut in half? That's not a straight forward answer. Because we measure time and distance in a similar way time would slow AND objects would contract proportionately making every reference frame measure the speed of light as c still (Lorentz Transforms do the same procedure and some VSL theories that match GR in all experiments also do). If space itself also contracts then no reference frame could detect any difference. However, if objects contract and time slows but space is static to observers that could look like space is expanding as travel time at any v between unbound objects increases (bound objects shrunk and time slowed). So light could be variable in a sense and match observation but according to all our theories we would never detect that variance locally. If any effect would be observed (like the observed expansion of space) it would not be a variance in c. So varying c globally could have an effect but we would have to call it something else because as observers within the universe we would not witness a variance in c. To say that a variance in c is causing some effect without experimental evidence for that variance would be a metaphysical stance. For example its very much possible that observers warp instead of a "space-time" background warping like in GR and that perspective can match all experiments done. However, science is performed through the looking glass of the observer who does the experiments so we choose that perspective as that's the best one we have.

Another way: Now hypothetically say the fundamental forces relative strength's change (or the fine structure constant changes). Changing the fine structure constant or manipulating the relative strengths of the forces can cause an observed change in the speed of light. This would change the "structure" of all fundamental clocks we have. This could change the observed speed of light.

The speed of light is also NOT constant in accelerating reference frames and is only constant locally in gravity. The speed of light is locally c because measuring rods and clocks are set locally.

 

[PeterDonis]

Distance is best measured by calculating how far a light ray travels in a unit of time.

This happens to be true now, which is why we currently define the meter in terms of light travel time. But it wasn't always true (and the meter wasn't always defined the way it is now--it used to be defined as the length of a standard piece of metal kept in France). So you can't base a general argument on it. See below.

Time is best measured by calculating how many back and forth vibrations light/fundamental forces do through a distance in some fundamental clock (vibrations of a Cesium atom for example).

That's not how atomic clocks work (see below). But even if it were, taking your two definitions together, they are circular, with no content: first you define distance in terms of light travel time, then you define time in terms of light travel distance. See the fundamental problem?

As far as how atomic clocks actually work, they measure the frequency of the light emitted when particular atoms undergo particular transitions between states. Any vibration of the atoms themselves is not measured (and indeed needs to be minimized, by cooling the clock to as low a temperature as possible, in order to get accurate readings). The frequency of the light is measured by measuring its energy and dividing by Planck's constant. No "vibration through a distance" is involved.

Could the speed of light even change from an observer's perspective if say its value were cut in half?

Sure, because for that to happen other constants would have to change too--mainly the fine structure constant. And there are ways of measuring those independently of any measurements of time or distance.

The speed of light is also NOT constant in accelerating reference frames and is only constant locally in gravity.

This has nothing to do with the topic under discussion in this thread. We are talking about the speed of light as it would be measured locally in an inertial frame.

 

[QST]

I do not think that the original questioner was concerned about units of measure or the numerical value of c in varying units. He was not interested in whether the speed of light is expressed in m/s or mi/hr or furlongs/fortnight. He was wanting to know why light travels at the speed that it does instead of some other speed expressed in the same units no matter what units you choose. Light travels 1 Planck distance in 1 Planck time because it is the nature of the universe for it to do so. If something were to move faster than that would we be able to measure it?

 

[Dale]

I do not think that the original questioner was concerned about units of measure or the numerical value of c in varying units.

Probably not, which is why we consistently point out that the question is really asking about the fine structure constant.

 

[PeterDonis]

If something were to move faster than that would we be able to measure it?

I don't see why not. We can measure times and distances accurately enough to detect possible "faster than light" objects over distances of a few hundred miles, if not shorter--that was the distance scale involved in the experiments some time back that at first appeared to show neutrinos traveling faster than light. (Of course it turned out that it was an error in the equipment, but the point is that the issue only arose in the first place because our measurements are accurate enough to spot possible faster than light objects at that distance scale.)

 

[vanhees71]

Probably not, which is why we consistently point out that the question is really asking about the fine structure constant.

The fine-structure constant is related to the electromagnetic coupling constant or the value of the elementary electric charge. This is just a parameter in the Standard Model of elementary particle physics, which has to be taking from experiment. Today there is no more fundamental theory that can explain this value. It has to do with the speed of light, because when using unnatural units, where ##\hbar c \neq 1## it is given by (in the usual HEP units, which are the Heaviside-Lorentz units):
$$\alpha_{\text{em}}=\frac{e^2}{4 \pi \hbar c},$$
which is a dimensionless quantity. After having fixed the values of ##\hbar## and ##c## by choosing your units, it just depends on the coupling electromagnetic coupling constant, ##e##.

The speed of light is indeed defined by choosing units for spatial and temporal distances. I think we have exhausted this topic by far now!

 

[Dale]

The speed of light is indeed defined by choosing units for spatial and temporal distances. I think we have exhausted this topic by far now!

Agreed!

 

[Dale]

For those who are still having trouble understanding the point being made about c and units, let's suppose that I told you that my car had a top speed of exactly 100 "vrooms". Now, I ask you, "let's fix the units of speed to be vrooms, I want to know why is my car's top speed 100 vrooms and can it change?" You would reasonably respond "well, how is the unit 'vroom' defined?" It turns out that the unit 1 vroom is defined as 1/100 th of the top speed of my car. So, now that I have defined my units I can unambiguously state that my car's top speed cannot change, it will always be exactly 100 vrooms and can never change. Why, because that is how I defined my unit of vrooms.

That clearly is an unsatisfactory answer, but it winds up being the only possible answer. If I didn't like 100 vrooms then I could make it 1 flubnubitz or whatever I liked, simply by changing my units. The reason that it is the only possible answer is because the question itself is dimensionful, so the answer inevitably depends on the units chosen to represent those dimensions.

A more interesting question is how my car's top speed compares to other speeds, such as the airspeed velocity of an african or european swallow. We can express the ratio of my car's top speed to the swallow speed as a dimensionless number which will be the same regardless of the units. We can then look at the physics to understand the things that would make a car's top speed a few times faster than the swallow's. So the question only becomes an interesting physics question once we start making a dimensionless comparison.

This is why when someone asks about the speed of light changing they are probably actually asking about the fine structure constant changing.

 

[PeterDonis]

Thread closed for moderation.

Edit: a whole bunch of off topic posts were deleted and the thread will remain closed.