Isn't the speed of light tautologically 299792458 m/s?

[Kekkuli]

A meter is defined as the distance that light travels in 1/299792458 of a second, so the speed of light is obviously always 299792458 m/s.

 

[Frabjous]

In a vacuum. Yes.

One always has to define units. The physics is in the fact that the speed of light is constant in a vacuum.

 

[phinds]

A meter is defined as the distance that light travels in 1/299792458 of a second, so the speed of light is obviously always 299792458 m/s.

Yes, but keep in mind that units are a man-made phenomenon that mimics nature in one way or another. The meter has had several definitions over the years meter

As @Frabjous has pointed out, that's not what's important and does not change the physics (just our description of the physics).

 

[Kekkuli]

The physics is in the fact that the speed of light is constant in a vacuum.

But, what if it wasn't constant in a vacuum? Because of the definition of meter, a statement just cannot be experimentally proven false when it is a tautology.

 

[phinds]

It would seem that you are asking "if modern physics were not correct, what would modern physics have to say about ... ?

https://www.physicsforums.com/insights/how-to-avoid-breaking-physics-with-your-what-if-question/

Or, alternately, you are asking "if we were to change our definitions of things, would our definition of things change?"

 

[Frabjous]

But, what if it wasn't constant in a vacuum? Because of the definition of meter, a statement just cannot be experimentally proven false when it is a tautology.

This definition of the meter is not what determines that the speed of light is constant. The speed of light was constant when the definition of a meter was a certain platinum bar or any of the earlier definitions.

 

[Kekkuli]

It would seem that you are asking "if modern physics were not correct, what would modern physics have to say about ... ?

https://www.physicsforums.com/insights/how-to-avoid-breaking-physics-with-your-what-if-question/

Or, alternately, you are asking "if we were to change our definitions of things, would our definition of things change?"

No. I don't think that's what I'm saying, but that the statement "The speed of light is constant" cannot be experimentally disproved in any way. That's not science. It's religion.
It follows directly from the definition of the meter that the speed of light is always constant in a vacuum. It's a tautology.

 

[Dale]

But, what if it wasn't constant in a vacuum?

Then you aren’t using SI. You are not required to use SI units if you don’t want to.

That's not science. It's religion.

It is a convention. Using a convention does not make something a religion. Don’t make stupid statements here.

Note: I am not calling you stupid just like you are not calling us a religion

 

[Kekkuli]

This definition of the meter is not what determines that the speed of light is constant. The speed of light was constant when the definition of a meter was a certain platinum bar or any of the earlier definitions.

Yes I know. But if the current definition of the meter implies that the speed of light is constant, then the claim that it is constant cannot be refuted.

 

[Dale]

Yes I know. But if the current definition of the meter implies that the speed of light is constant, then the claim that it is constant cannot be refuted.

Not true. You can just use some units other than SI units.

 

[PeroK]

Yes I know. But if the current definition of the meter implies that the speed of light is constant, then the claim that it is constant cannot be refuted.

If the speed of light wasn't invariant, then the definition would not work. For example, if you tried to insist on Newtonian space and time as a definition, then you would be undermined by experiments.

The test of a lot of physics isn't in the fundamental definitions themselves, but whether the extensive theoretical structure build on top of those definitions and laws stands up.

You can never prove a postulate. But, if you choose the wrong postulates, then your theories build using those posulates will fall down experimentally.

 

[PeterDonis]

But, what if it wasn't constant in a vacuum?

This would contradict the laws of physics. It's meaningless to ask what the laws of physics say about something that contradicts the laws of physics.

Because of the definition of meter, a statement just cannot be experimentally proven false when it is a tautology.

You can't change the physics by making unit definitions. The actual physics involved is:

(1) Spacetime has a particular geometric structure that includes light cones at every event. The actual physical meaning of "the speed of light in vacuum is constant" is "the local light cone structure of spacetime is the same everywhere". That was true even before the SI definition of the meter made the SI numerical value of the speed of light a defined constant instead of an experimentally measured quantity.

(2) Electromagnetic radiation travels along the light cones in spacetime. That is why we can use light to probe the geometric structure of spacetime (which itself does not depend on light for its existence). The key property of light that makes this possible is that the photon is massless. That, again, is a property of the electromagnetic field that was just as true before the SI definition of the meter made the speed of light in vacuum a defined constant.

 

[Sagittarius A-Star]

But if the current definition of the meter implies that the speed of light is constant

The definition of the meter via the old meter prototype in Paris had the same property.

This can be argued via the Bohr radius.

The length of the old meter prototype $L_1$ is a multiple (factor := $k$) of the Bohr radius $a_0$:
$L_1 = k * a_0 = k * \frac {\hbar}{m_ec\alpha}$.

Source:
https://en.wikipedia.org/wiki/Bohr_radius

=> $\ \ \ c = k * \frac {\hbar}{m_e L_1 \alpha}$

So, if $L_1$ is assumed to be "constant with time", then you will measure a constant $c$.

 

[PeterDonis]

This can be argued via the Bohr radius.

This argument assumes that the fine structure constant $\alpha$ is the same everywhere. Both our best current theory and our best current experimental measurements say that it is. But it's worth noting that this, again, is a physical property of the electromagnetic field and its interactions with matter, and does not depend on any choice of units ($\alpha$ is a dimensionless number which is the same in every unit system).

 

[Frabjous]

Yes I know. But if the current definition of the meter implies that the speed of light is constant, then the claim that it is constant cannot be refuted.

Look carefully at the definition. It contains a high precision value for the speed of light, not the speed of light itself. If the speed of light changed, one would still be able to measure it using this definition.

 

[Ibix]

Let's say I build an old school meter rule, by dividing the circumference of the Earth in 40,000,000 equal parts (edit: number corrected, with thanks to PeterDonis - see next post). Then I use the ruler in some experiment A to measure the speed of light, then in some different experiment B to measure the speed of light. Then I ignore those results and define the speed of light to be $c=3\times10^8\mathrm{ms^{-1}}$ and use experiment A to construct a new meter rule and experiment B to build a new meter rule.

If there were circumstances under which A and B gave different measures of the speed of light with my old school ruler then the two rulers I built after my definition would be different lengths when put next to each other. So if it were wrong to assume that the speed of light in vacuum is constant and invariant the error remains detectable - it's just that you compare the lengths implied by the modern definition instead of comparing the speeds implied by the old.

 

[PeterDonis]

Let's say I build an old school meter rule, by dividing the circumference of the Earth in 400,000,000 equal parts.

Actually it's 40,000,000.

 

[Ibix]

Actually it's 40,000,000.

What? Next you'll be telling me $c$ isn't $3\times 10^9\mathrm{ms^{-1}}$!

Will edit above - thanks.

 

[Vanadium 50]

How do we know the frequency os a Cs atom is 9 192 631 770 Hz? Isn't that tautological?

 

[vanhees71]

We define the second by this value of this frequency. That's a definition of the unit and no tautology. Then to define the unit of length we fix the value of the speed of light when time is measured in seconds an length in the to be defined unit of metre. In this way also the other base units are built up step by step by setting values to the fundamental constants as $h$ (->kg), $k_{\text{B}}$ (->K), $e$ (->C=A s), N_A (-> mol). There's no tautology anywhere. It's enabling the physicists to realise the units with ever higher precision by ever more precise measurement devices.

 

[Nugatory]

But, what if it wasn't constant in a vacuum? Because of the definition of meter, a statement just cannot be experimentally proven false when it is a tautology.

If the speed of light were not constant for all observers the definition of the meter in terms of light travel time would have been rather unsatisfactory and the metrologists would likely not have chosen it.

Experimental evidence that the speed of light is the same for all observers was plentiful and convincing long before the modern definition of the meter was chosen.

 

[Dale]

There's no tautology anywhere.

I do agree with the sentiment. There is no important tautology. But of course in the strictest sense any definition introduces a tautology since all definitions are tautologically true by definition.

 

[PeterDonis]

all definitions are tautologically true by definition

Which, I take it, is also a tautology?

 

[dextercioby]

A meter is defined as the distance that light travels in 1/299792458 of a second, so the speed of light is obviously always 299792458 m/s.

I hope what I write below has a bit of novelty with respect to the other comments you received above:

Here is the deal. Let's analyse the definition of the meter/metre from a logical/content perspective. "A meter is defined as the distance [presumably in ordinary 3D flat space, but I let the SR/GR experts here comment on this hidden assumption] traveled by light (electromagnetic radiation) in 1/299792458 seconds."

How many concepts do we have here? Three, meter, distance and second. So the meter is a unit of distance and distance has its own definition. No problem. Then the meter is defined with respect to the unit of time through a sharply defined number (fixed, by convention has been stripped of decimals and uncertainty). So, in order to have the definition of meter free of c i r c u l a r i t y (quite a different concept to t a u t o l o g y), we must define the second elsewhere independently of (units of) distances, i.e. meters/metres. And we define the second in terms of a particular (again sharp, no decimals, no uncertainty) number of cycles in a hyperfine transition of a Caesium atom, so our definition of meter as given passes the circularity test.

So what is the logical content of this definition? Yes, the definition of meter implies (logical deduction/deductive inference) that the speed of light must be 299792458 m/s. So it's a (unit of distance) ==> b (speed of light) in terms of a. Now what about the opposite inference? b (speed of light) in terms of a (definition of meter). Well, the definition of speed is "distance traveled in unit time", so the unit of speed is defined in terms of a unit of distance (meter), and a unit of time (second). The trick is here that, if one uses the post 1983 definition of meter, there is a circularity in the definition of the speed of light which we were forced to have by defining the meter indirectly in terms of the speed of light. So the new definition of meter is not circular, but the inference it creates brings up a circular definition of the speed of light. And this is still not a tautology. One can argue that speed is a derived concept, so it's obvious that it only works to define units of speed in terms of fundamental quantities such l as units of lenght and time, not the otherway around.

What is a tautological definition? "A book is a type of book with a certain number of pages". That is a is defined in terms of a. What is a circular definition? "A book is a binding of a number of pages". "A page is an element which is bound in a book". This is circularity, a is defined in terms of b, which in turn is defined in terms of a.

 

[pervect]

A meter is defined as the distance that light travels in 1/299792458 of a second, so the speed of light is obviously always 299792458 m/s.

Rather than being a tautology, I'd describe it as being a standard. Specifically, a standard created by BIPM. the international organization established by the "treaty of the Metere", signed in 1875. SI has also adopted the BIPM definition, as has most everyone else that I am aware of. Thus, if you buy a distance measuring device (ruler) traceable back to your national bureau of standards that standards bureau most likely uses the BIMP defintion.

There have been in the past other definitions of the meter in the past. Old textbooks, when they talk about measuring the speed of light, for instance, date from the time when the meter was defined differently. Most likely it dates from the time when the meter was defined by a prototype bar, but there have been others, the initial defintion was based on the circumference of the Earth, for instance.

There's quite a long and interesting history of the evolution of the standards.

I believe the vesion you quote has been supreceeded. The www gives the current defintion as:

The metre is defined by taking the fixed numerical value of the speed of light in vacuum, 𝒸, to be 299 792 458 when expressed in the unit m s−1, where the second is defined in terms of the caesium frequency $\Delta v$.

 

[Vanadium 50]

This thread start has a whiff of relativity denialism about it "Gosh, those stupid scientists don;t even know they have a tautology!"

Some facts, hopefully not in dispute:

1. Standards change over time. The length of the king's foot is not a good standard, so we don't use it any more.
2. Standards based on artifacts are undesirable. Your artifact can be lost, damaged, altered by time and it can only be in one place at a time. Standards based on physical constants don't have this problem.
3. Presently, time measurements are more accurate than pretty much anything ekse you care to measure,

The current SI is based on a set of constants. They were chosen because after over a century of observation, we have not seen them change. It's not just the soeed of light: it's Planck's constant, the charge on the electron, etc.

If, despite the centuries of theoretical and experimental progress, we found a place where measurements of c came out differently, yes, we would interpret them as a change of duration of the second. Is this "wrong"? You would need to describe exactly what measurement you were doring and why "change in c" is a better description than "change in the second (or meter)". Without that, we can;t have a serious discussion about implications, can we?
.

 

[pervect]

This thread start has a whiff of relativity denialism about it "Gosh, those stupid scientists don;t even know they have a tautology!"

It could be - it's hard to say. But the discussion has seemed rational so far, which is IMO all we can ask.

I wish I knew more about history - I think some of the history about how and the BIPM, and as a consequence the scientific community at large, came to accept the speed of light as a standardized constant rather than something we measure would be very interesting and useful. Getting large bodies to agree on pretty much anything is quite difficult, as I think many recent events suggest. And it'd be interesting to have some account of how that process occurred. I suspect that the actual history would be a bit different from the idealized history that I'd imagine - the actual history of science is usually a lot more complex and random than the logical progression that is frequently described.

I actually think it is important to realize that we don't measure the speed of light anymore, but that it's defined as a constant. It's equally important to realize that we haven't always done things that way. Many textbooks nowadays still talk about the speed of light as if it were something that could be measured, even though we don't do that anymore.

To go back to my historical observations - I'm pretty sure there was a lot of debate on this question when the change was made by the BIPM, but I'm afraid I don't have any details, though I vaguely recall glimpsing something about the existence of such discussions. We do know what the ultimate decision was, however.

To address the issue of "tautology", we have not limited the discussion by changing our definitions. Rather, by changing the definitions, we've changed how we talk about the underlying fundamental question. For instance, we could ask questions, such as "does the length of the old prototype meter bar change with regards to our new standards". The answer would be yes, but not (so far as we know) in any sense that detracts from our current standards. For instance, our original prototype might get dirty, changing it's measured length. And cleaning it is problematical, that process also has the potential to change it's length by removing some material of the original bar as well as the dirt. Back in the day when it was the standard, people had to worry about such issues, but we don't worry much about them much anymore. Similarly, we can ask about mechanical deformations to applied forces. It's clear that our prototype would in fact deform, and nobody (as far as I know) seriously suggests that the fact that our prototype deforms invalidates the very idea that distance exists. But it does leave some questions about how we might think about length in extreme environments (high gravity, rapid rotations, for example).

Note that we can't possibly address all the different ideas of what people might mean by length if they don't mean the current standard, but I find the meter bar prototype an interesting choice to talk about. I've come to realize that it's more important for people with some philosophical bent to actually think about what they think they mean when they talk about distance, rather than to get into any specifics.

"Rigid objects" as a possible abstract idea (rather than our physical prototype meter bar) is another interesting possibility. However, it turns out that that idea has quite a few problems, which would take a post at least as long as this one to properly address. Spoiler alert - there isn't any such thing that physically exists, and there are non-obvious conceptual issues as well. If one go into the studying of special relativity with a pre-concrived notion of distance based on the idea of rigid objects, one is likely going to run afoul of the Herglotz-Nother theorem at some point along the journey.

So, what I try to do is to encourage people who have some questions is to think about what they actually mean by length and distance. Typically, I don't see any response to the question when I ask it, so it's hard to guess what people's thoughts might be. How much of this sort of discussion is appropriate to discuss here on PF is also a question, but it hasn't been an issue - typically, as I said, raising the issue , while useful IMO, doesn't result in any response or debate.

 

[Ibix]

So, what I try to do is to encourage people who have some questions is to think about what they actually mean by length and distance.

Isn't the point that the change to unit definitions has changed how we think of distance (at least in the formal sense)? With a physical object as the definition of the meter you're defining distance as a fundamental thing. Coupled with a definition of a time unit, speed is a derived quantity. But in the modern definition, speed and time are the fundamental quantities and length is a derived quantity. In fact, if you track through the definitions, "I'm travelling at 30m/s" actually means "I'm travelling at one ten millionth of $c$", completely independent of the definition of the meter.

Distance is now fundamentally "what radar measures", whereas before it was "what rulets measure".

 

[Vanadium 50]

Isn't the point that the change to unit definitions has changed how we think of distance (at least in the formal sense)

I don't think so. While it is true that the speed of light is now usually thought of as a historical remnant, like measuring depth in fathoms and distances at sea in nautical miles, the choice of standards is more about how they are realized. When we changed from Amperes to Electron Charge, it wasn't because after a century we finally believed electrons exist: it because charge finally because a better unit than current.

 

[Drakkith]

Yes I know. But if the current definition of the meter implies that the speed of light is constant, then the claim that it is constant cannot be refuted.

You have it backwards. We've used the distance that light travels in in a unit of time to define a unit of distance. The meter. I could do something similar with my car. I get the car up to the point where the speedometer says 50, then I define the 'cargofar' as the distance that my car travels in two seconds. Now the unit of cargofar is related to how fast my car travels in two seconds when the speedometer says 50. If I then decide to change the size of the tires on my car without changing the speedometer, then the length of a cargofar also changes, because I've defined it based on what my speedometer reads.

Of course, I want to make the cargofar unit more widespread, so I make everyone calibrate their own speedometers to mine. But then we have the issue that even after calibration each speedometer is still slightly different, leading to different lengths of a cargofar for each speedometer.

The beauty of defining the meter off of the speed of light is that the speed of light doesn't change as far as we know. So we don't have to worry about using 'speedometers' that are all different and thus measuring the meter differently.

 

[vanhees71]

I don't think so. While it is true that the speed of light is now usually thought of as a historical remnant, like measuring depth in fathoms and distances at sea in nautical miles, the choice of standards is more about how they are realized. When we changed from Amperes to Electron Charge, it wasn't because after a century we finally believed electrons exist: it because charge finally because a better unit than current.

There's of course a difference between the definitions of the units, which now are pretty abstract, i.e., by just defining the numerical values of the "fundamental constants" (of our contemporary best body of knowledge). It's another question, how to realize and with which precision these units. That's why in addition to the pretty short definitions you have entire brochures for "mise en pratique", i.e., how the units are realized by real-world high-precision measurements:

https://www.bipm.org/en/publications/mises-en-pratique

What I find very interesting about discussions like this is the interplay of theory and experiment, i.e., the definition of the units always must depend on some theory.

If one thinks about it the history of the SI units reflects this clearly. E.g., originally the base units were time, distance, and mass, and indeed that was what was needed for Newtonian mechanics. One fundamental law was Newton's universal law of gravitation, and indeed that was used to define the units of time in terms of the motion of the Earth around the Sun and distance in terms of the length of a specific longitude of the Earth and mass via the mass of $1 \, \text{dm}^3$ of water (either at the melting temperature of ice or at the temperature of maximal density):

https://en.wikipedia.org/wiki/Second#History_of_definition
https://en.wikipedia.org/wiki/History_of_the_metre
https://en.wikipedia.org/wiki/Kilogram#Timeline_of_previous_definitions

These definitions have been changed over the time several times. This happens whenever the older standards don't hold up anymore the accuracy one can measure the corresponding quantities due to technological advancements.

 

[hutchphd]

But, what if it wasn't constant in a vacuum? Because of the definition of meter, a statement just cannot be experimentally proven false when it is a tautology.

A system of units is exactly that, no more and no less. If your system defines units of length to be relative to a platinum bar in a vault, how do you know that its length is not "actually" changing when you close the door of vault? The purpose is to allow us to compare measurements over time and space in the most precise and useful way we can apprehend. Apparently one must choose some standard(s) as immutable and constant. The choice is one of utility, not dogma.

 

[pervect]

Isn't the point that the change to unit definitions has changed how we think of distance (at least in the formal sense)? With a physical object as the definition of the meter you're defining distance as a fundamental thing. Coupled with a definition of a time unit, speed is a derived quantity. But in the modern definition, speed and time are the fundamental quantities and length is a derived quantity. In fact, if you track through the definitions, "I'm travelling at 30m/s" actually means "I'm travelling at one ten millionth of $c$", completely independent of the definition of the meter.

Distance is now fundamentally "what radar measures", whereas before it was "what rulets measure".

I suppose distance has changed some, but I view most of the changes in special relativity as being related to how we think about time. Certainly, the inter-relationship between distance and time is new. Changing the standard doesn't seem like as big a deal to me as the conceptual changes related to the unification of space and time.

On the practical side of things, the changes in standardds are a foundation for more precise measurements. The old standards had limitations that were holding back our ability to improve precision - I believe that this is the primary reason that the BIPM changed them. I..e. the changes were made for practical and functional reasons, not ideological ones.

 

[Dale]

I believe that this is the primary reason that the BIPM changed them. I..e. the changes were made for practical and functional reasons, not ideological ones

That is my understanding also. The platinum bar was retired because using the speed of light gave a more reproducible meter.

 

[Vanadium 50]

Ah...PF..where every discussion turns to metrology.

Meter-standard-as-an-artifact ended in the 1960's. It was replaced by a certain spectroscopic line of krypton. The second used to be defined by the earth's average rotation, and was replaced by the atomic clock definition in the 1960's as well. Both were significantly later than the concept of spacetime. The present definition was not because we all suddenly agreed that SR was a good idea. It was because we could measure time far more accurately than distance, and this was likely to remain so for the foreseeable future.

Speaking of which, the OP seems not be participating in this or any of his other threads. I'd call it a drive-by, but don't want to get into a discussion of what the proper velocity standard should be.