speed of light

russ_watters

DrMatrix, you are harping on the fact that the meter is defined by the speed of light and its been explained to you several times now that that is irrelevant to the question of if the speed of light is constant. Exploring this point by Integral a little more may be useful:
The speed of light has been known (or at least expected) to be constant for a hundreds of years. The meter was defined in terms of the speed of light only 20 years ago. The meter is tied to the speed of light because the speed of light is a universal constant, not the other way around.

In fact, the reason that the meter is no longer defined as the distance between two scratch marks on a bar of metal in France is that since about 20 years ago, our abiliy to measure the speed of light accurately has exceeded our ability to measure the distance between those two scratch marks accurately. As well, due to environmental factors, the distance between those two scratch marks wasn't even constant. The meter had to be re-defined in terms of something more constant/precise or it would hinder scientific research. The speed of light quite literally makes a better meter-stick than the meter-stick does.

If you really want to argue arbitrary units, how about the definition of a second...?

Jack Martinelli

Why do that? Why not define a ruler in the general sense so that it can be used to measure intervals that are space-like or time-like.

Integral

I do not see the circularity here. Yes, the question has changed but unless a measurement of c is involved in the experiment to find [tex]\epsilon_0[/tex] it is not circular.

turin

quoting Integral:
It is not a matter of what, but how.




quoting Integral:
How do you know this? Compared to what?




quoting Integral:
How do you know this? Compared to what?




quoting Creator:
Would that I could.




quoting Integral:
Say WHAT?! How do you define a coordinate system? I admit there are other ways to define one, but there must be one. Or, in the words of DrMatrix:



quoting Integral:
Of course it matters. It matters for the same reason that most of you seem to be saying it doesn't. If the speed of light is taken to be the standard, then it is a constant by definition, which answers the original post, unless, by "speed of light," the original poster meant something other than "c."




quoting jdavel:
What do you mean, "you'd never do that"? That is exactly what would be done. How else would you calibrate length?




quoting russ_watters:
That's the point. Except, I would replace "constant/precise" with "universal;" the length of a rod is almost as constant and just as precise as the consant in the wave equation before we impose a scale on it. There isn't a rod for calibrating the meter locked in a vault and held at strict environmental conditions on Mars, but it is believed that Maxwell's equations can be found on Mars. Thus, they give us the standard, but it is still just a standard. I'm not saying that the equations are merely a standard (they are physical law), but the numerical value that we infer from the wave equation is defined as a standard universal constant. It is a constant because we have defined it that way. We have defined it that way because it is believed to be universal, and therefore more convenient than using a bar.

Integral

Since the definition of the meter is tied to the speed of light, if the speed of light were to change, the length of the standard would change. This means that if I were to use the standard meter to measure a known distance, I would come up with a different distance after the change in c. It would now be 60km to London it was 50km beforeI find this comment very interesting. What "fancy" equations are we talking about? A square root??? If you consider the square root to be a "fancy equation" then the relativity understand so well is full of "fancy equations". I am afraid that anyone who considers the square root to be a "fancy" equation simply cannot comprehend the even the simply math used in the development of Special Relativity. Lets not say anything of the very difficult math required to understand General Relativity. By the way, since you are so enamored with the definition of a specific coordinate system you should realize that on of the important features of GR is the ability to express the Physical relationships in a manner that is independent of the coordinate system. In the fundamental expressions look the same in ALL coordinate systems.

turin

And that would show what? What's the big deal? Do you believe that lengths should be invariant in themselves? In SR, using the speed of light as a standard causes lengths to change. Is that wrong, too?

Integral

The whole point of the standard coordinate system you carried on about in your previous post is so that the standard length does not change. Now you seem to be arguing the other side of the coin. Make up your mind. Perhaps I do not understand your point. Lengths in SR change with relative velocity, if there is no relative velocity there is no length change. What has SR to do with the current discussion? I have asked this question over and over, never get an answer.


Suppose I were to define a standard volume of water as the amount of water in a certain bucket. Then using that bucket I measure the volume of several other buckets to be 5 standard buckets. One day I see a new shiny bucket that I would rather use as my standard. When I use my new standard to measure the amount of water in one of the previously measured buckets I find that it now holds 6 standard buckets. Are you telling me I should ignore this discrepancy or should I assume that all buckets have somehow changed? Clearly, if it is indeed used, a change in a standard will be noticed.

If the meter were never used to measure anything but the speed of light we would indeed never notice the change. But as soon as we apply the standard to something else we will certainly notice if the standard changes. Suddenly all previous measurements will be wrong according to our standard.

DrMatrix

What is a "known distance"? A distance is known only when compared to the standard of length. The meter is the standard. If the distance to London was 50km and it is now 60km, then the distance to London changed. The meter is still one meter.

Yes I am well aware that GR allows aribtrary coordinates systems. I didn't want to get into that. You can't talk about a constant speed of light in GR. I was being sarcastic, I thought you'd get that. Sorry.

Integral

Please explain further what you mean, I don't get it.
It is believed that the oil we are burning today was living plant life in the era of the dinosaurs. It has an atomic structure that is compatible with our current chemistry. Therefore atomic structure has not changed since the era of the dinosaurs, therefore the speed of light has not changed (significantly).

Simply citing the current state of Physics. It may be that c has changed over the life time of the universe, but that is not the current understanding.


Ok, we need to establish a coordinate system. Now what is the significance of that coordinate system? What part does the coordinate system play in the final work of relativity?
Precisely, none. General Relativity allows expression of physical laws independent of the coordinate system.

How does the fact that the meter has been tied to the speed of light effect the speed of light? The key point to this entire discussion is the difference between
"the speed of light is constant because the meter is defined in terms of the wavelength of light?

and

"The meter is expressed in terms of the wavelengths of light because the speed of light is constant"

I think you are stepping beyond the Physics into philosophy and semantics here. The speed of light is a universal constant. Please take debates about this issue to Theory Development.

turin

What standard coordinate system? I simply supported DrMatrix' position that there must be a coordinate system. I even alluded to the possibility of other ways to define a coordinate system indicating that I do not think a lattice of rigid rods is a standard.




It provides an example to show that there is no problem with the spatial distance between any two points in space, such as the distance between two cities, changing.




But this is just like changing from yards to meters. There is no problem here; it is just a matter of a conversion factor. What would make your example more interesting is to say:

What if we measured the amount of some water in terms of the number of standard shiney buckets full, and found it to be six one say, and then, the next day, the the amount was only five. Well, then we'd have to discard our conservation of water law, right? No, because, just in the nick of time, a genius comes along with an incredible breakthrough. He (or she; there have been female geniuses, too) declares that the amount of water is not determined by the volume, but by the weight. Now, whenever the water is measured, on whatever day, the weight is always found to be 8.3 standard shiney buckets. Hooray for the inovative minds on the standardization committee!

Integral

There certainly is a problem with distances changing if it is due to a change in the standard. Why to you think that the US mileage signs are mileage signs and not km signs? A change in a standard requires a lot of re calibration this costs money. Sorry to bring real world issues into the argument.

I feel that there is a issue with the distance changes between cities, if standards mean anything, when I measure a distance in meters it had better read the same today as it did yesterday or next year. That is the whole point of a standard.

When London is moving at .5c wrt to Paris then I would expect the distance to change. As long as they are stationary the distance must remain the same. The distance is a physical quantity it does not change with the units you measure it in.

turin

Consider defining distance against a standard rod. What is the prescription for measurement? Do we place the rod at rest along side the distance to be measured? If this is the method, then all we can do is put the distance in three categories: shorter, longer, same length as standard. Of course, this simply won't do, so we can translate the rod along the distance. This is, of course, inconvenient. For instance, this is impractical to measure microscopic distances and interstellar distances with the same standard. Also, translating the rod takes time. Things can change in time. Nothing fundamentally guaruntees that the object being measured will not change significantly during the process of translation.

By what, I mean the trivial issue of the standard itself. By how, I mean the more significant issue of the method used to compare to the standard.




I don't understand how you jumped from atomic stucture to speed of light.




But this still doesn't answer the question, "compared to what?"




Expression of physical laws is math. In order to do physics, there is no way around a coordinate system. Therefore, the coordinate system becomes significant, and in GR quite non-trivial.




I don't support the first justification, if "speed of light" is intended to mean "c."

I support the second statement, but it is not an answer to the original post.




Did I ever once disagree with c as a universal constant? I don't visit the theory development thread for two reasons: 1) I'm not interested in other peoples attempts to disprove relativity and 2) if I actually thought I had a sound theory to develope, I wouldn't post it on the internet to invite someone else to steal it from me and take all the credit.

Integral

Turin,
I am failing to see the point of your posts or your arguments.

Jack Martinelli

The circularity is: if [tex]\mu_0[/tex] and [tex]\epsilon_0[/tex] are constant it is because c is constant, which is constant because [tex]\mu_0[/tex] and [tex]\epsilon_0[/tex] are constant which is constant because...

turin

Are you, really, or are you being sarcastic. It seems like you're being sarcastic. Well, shame on you.




So do I. It shows that, if the distance between New York and Miami changes by a significant percentage in the course of a day, I'd better run for the west coast. One of the last things I would personally do is blame a standard for changing. Oh ya, and, sarcastically, I'm sorry for bringing the good old U.S. of A. into the argument.




That's the whole point of defining that particular distance as a standard distance. Standards have different points depending on the application. But I don't agree that the point of a standard of one unit is to make sure that some arbitrary property of some arbitrary object remains constant.




But they are never stationary, even WRT each other. As far as I know, the distance between London and Paris is not a standard, nor is it even assumed to remain constant, in the physics that I've studied. It is a reasonable approximation, but not a constant standard value.




It does if you first measure it in units of length, and then subsequently measure it in units of time. It completely changes in meaning. If you say that the space-like separation of London and Paris is x km, that implies that they are causally disconnected in that context. But, if you say that Paris is y hrs from London, you are talking about how much time you would experience during the flight or train ride from London to Paris. These two measurements/units have completely different physical meanings, but they both measure the distance between London and Paris.

Integral

The experimental methods used to measure a value for [tex] \epsilon_0[/tex] are significantly different from those used to measure c.
The fact is with modern technology I believe it is easier to get a precise measurement of c then [tex] \epsilon_0[/tex] so it may well be that it is now defined it terms of c then the other way round.

That does not change the fact that [tex] \epsilon_0[/tex] is a basic property of space time which is a factor in the propagation of EM waves.
Which is the "more" fundamental constant. I personally do not know.

Integral

Turin,
You are now arguing semantics, can we get this thread back on topic.