Speed of Light Puzzle: Is c a Localized Value?

[Orodruin]

And the fact that we've taken millions of measurements of the speed of light within the observable universe and always got the same result allows us to infer the speed of light within the observable universe when it's not being measured.

Again, you do not measure the speed of light.

 

[jbriggs444]

It does. And the fact that we've taken millions of measurements of the speed of light within the observable universe and always got the same result allows us to infer the speed of light within the observable universe when it's not being measured.

However, it doesn't allow us to infer anything about the speed of light outside the observable universe,

I would disagree mildly. We can infer something about the speed of light [fine structure constant or other property] outside the observable universe. We just can't test that inference. There could be some different behavior outside the observable universe just like there could be some different behavior for tomorrow's sunrise. In both cases there is no reason to expect a discontinuity in behavior and no certain knowledge that precludes the existence of such a discontinuity.

 

[GuyBarry]

Again, you do not measure the speed of light.

Well you can't measure the speed of light now, because it's a defined constant (in SI units). But lots of measurements were taken prior to the time that its value was defined - otherwise there'd be no basis for the value that's currently agreed on.

 

[Orodruin]

Well you can't measure the speed of light now, because it's a defined constant (in SI units). But lots of measurements were taken prior to the time that its value was defined - otherwise there'd be no basis for the value that's currently agreed on.

Using different units conveniently chosen so that they more or less corresponds to the ones we use now.

The point I believe is missing many times is that people confuse the speed of light being invariant with it being constant. The first is a deep physical insight, the second is a matter of definition of units.

 

[GuyBarry]

Using different units conveniently chosen so that they more or less corresponds to the ones we use now.

You're getting it back to front. The units we use now were conveniently chosen so that they more or less correspond to the ones that were used previously.

Over its history the second has been defined in terms of the rotation of the Earth, in terms of the Earth's orbit round the Sun, and (since 1967) in terms of properties of the caesium atom. The metre has been defined in terms of the circumference of the Earth, in terms of a physical artefact, in terms of properties of the krypton atom, and (since 1983) in terms of the second and a fixed numerical value for the speed of light.

There have been over three centuries of experiments to determine the speed of light. It was only relatively recently in scientific history that sufficient data was collected confirming the value of the speed of light to allow it to be adopted as the standard for measurement.

The point I believe is missing many times is that people confuse the speed of light being invariant with it being constant. The first is a deep physical insight, the second is a matter of definition of units.

I appreciate that they're different concepts, and you're right to point out the potential for confusion between them. Could you theoretically have a speed of light that was invariant in all inertial reference frames but not constant?

 

[GuyBarry]

I would disagree mildly. We can infer something about the speed of light [fine structure constant or other property] outside the observable universe. We just can't test that inference.

And therefore any such inference must be unscientific.

I have no objections to people formulating theories about what exists outside the observable universe, but it doesn't constitute "science" as I understand it.

 

[Ibix]

You're getting it back to front.

You are missing @Orodruin's point. A meter is roughly as far as our monkey arms reach. A second is roughly how long it takes our monkey hearts to beat. The invariant speed at which light travels is simply the unit conversion factor between time and length - so in SI units it's roughly the ratio of the length of one monkey heartbeat to one monkey arm length.

What would it mean to change the speed of light? Could be several things.

First, it could mean that light doesn't travel at the invariant speed - i.e. photons aren't massless. I believe the current experimental bound on their mass is around 10^-50kg, but it's still possibly non-zero. In that case photons wouldn't have a single defined speed, so this probably isn't what you mean.

Second, it could mean that you want to use different units - maybe you could use so called geometric units such as seconds and light seconds, so c=1. This is obviously trivial and changes nothing, so it probably isn't what you mean either.

Third, it could mean you want to change the ratio of one monkey heartbeat to one monkey arm length. Not just by breeding a longer armed monkey, but by altering fundamental physics so that hearts in general beat slower. It turns out that what you actually want to do is vary the fine structure constant. If you keep that fixed, doubling the speed of light changes other constants to do with electromagnetism such that our monkey arm lengths double and the speed of light remains 3×10⁸monkey arm lengths per monkey heart beat. Varying the fine structure constant let's you change the ratio, and I suspect this is what you actually want to think about.

And therefore any such inference must be unscientific.

I have no objections to people formulating theories about what exists outside the observable universe, but it doesn't constitute "science" as I understand it.

You are missing the point here too. We construct a model of a homogeneous universe (which turns out to imply finite but unbounded, flat, or open - but flat matches observation best) because it's simpler than any other model and pretty much consistent with what we see. The hypothesis being tested is not "is the universe infinite, flat, and homogeneous" but "is the universe experimentally distinguishable from our model of an infinite, flat, homogeneous one". If it's not distinguishable then our model is good (whatever the truth is about the unobservable stuff). If it is distinguishable then we need to revisit something. So far it works, with a bit of tweaking. Sure we could develop models that do other stuff outside the observable universe, but why bother? We can't test it.

 

[GuyBarry]

A meter is roughly as far as our monkey arms reach. A second is roughly how long it takes our monkey hearts to beat.

Neither of those is true.

The definition of the second goes back to around 1000 AD. It was based on the theory that the period of the Earth's rotation was constant. That period was divided into 24 hours, each divided into 60 minutes of 60 seconds each. So the original definition of the second was 1/86400 of the period of the Earth's rotation, and this lasted right up until the mid-20th century after it had been demonstrated that the Earth's rotation was slowing down.

The intended definition of the metre - first proposed in the 17th century - was the length of a pendulum with a half-period equal to one second. However it was discovered that this definition was dependent on fluctuations in the Earth's gravity, and so in the late 18th century a definition relating to the Earth's circumference was adopted - one ten-millionth of the distance from the North Pole to the Equator, along the meridian passing through Paris. There have been several redefinitions since then, as I mentioned in an earlier post.

The invariant speed at which light travels is simply the unit conversion factor between time and length - so in SI units it's roughly the ratio of the length of one monkey heartbeat to one monkey arm length.

The first quantitative estimate of the speed of light was made by Ole Rømer in 1670, by observation of the periods of one of Jupiter's moons. Since then it's been refined by centuries of experimentation. Michelson's 1926 experiment determining the speed of light between Mount Wilson and Lookout Mountain was probably the original basis for the value we use today, but it took until 1983 until the current standard was adopted.

What would it mean to change the speed of light?

It's difficult to know. The values of so many other physical constants are related to the speed of light that any change would have huge consequences on the rest of our theories of physics.

It turns out that what you actually want to do is vary the fine structure constant.

I don't actually want to do anything. I am simply saying that if the value of the speed of light - or indeed the fine-structure constant, or anything else - were different outside the observable universe, we'd have no way of gathering any evidence.

The fine-structure constant, being a dimensionless constant, is independent of any system of units, and so I suppose it's in a sense more fundamental than the others; but we're no more able to gather evidence of the value of the fine-structure constant outside the observable universe than of any other value.

You are missing the point here too. We construct a model of a homogeneous universe (which turns out to imply finite but unbounded, flat, or open - but flat matches observation best) because it's simpler than any other model and pretty much consistent with what we see.

Indeed - Occam's razor, as has been mentioned before. That's a philosophical principle though, and not a scientific one.

The hypothesis being tested is not "is the universe infinite, flat, and homogeneous" but "is the universe experimentally distinguishable from our model of an infinite, flat, homogeneous one". If it's not distinguishable then our model is good (whatever the truth is about the unobservable stuff). If it is distinguishable then we need to revisit something. So far it works, with a bit of tweaking. Sure we could develop models that do other stuff outside the observable universe, but why bother? We can't test it.

No we can't. And that's why any theory of what exists outside the observable universe is unscientific.

It may well be that the universe is not experimentally distinguishable from our model of an infinite, flat, homogeneous one, but also that the universe is not infinite, flat, and homogeneous. And there's no way of experimentally falsifying that hypothesis.

Ultimately, there are limits on what we can know about the universe, and any theory outside those limits is not a scientific theory.

 

[PeterDonis]

I have no objections to people formulating theories about what exists outside the observable universe, but it doesn't constitute "science" as I understand it.

It depends on what you mean by "theories about what exists outside the observable universe".

If you mean a theory that says something like: "Things are one way within our observable universe, but suddenly change into something completely different as soon as you cross the boundary into the unobservable universe", yes, I would agree that would be unscientific.

If you mean a theory that says something like: "The simplest model of the universe that accounts for what we can observe does not have a boundary at the edge of what we can observe; therefore it is simpler to assume that things just continue on the same way past the boundary", then no, I do not agree that that would be unscientific. The absence of the boundary is not just put in by hand; it emerges from the same theoretical assumptions that you have to make to account for what we do observe.

 

[Ibix]

Neither of those is true.

My reach is about a metre. My heartbeat is around sixty per minute. Whether that's the definition of the metre or the second isn't important. Replace every instance of "monkey arms" with "some fraction of the Earth's circumference" and "monkey heartbeat" with "some fraction of a day" if you want. It changes nothing about my argument.

The first quantitative estimate of the speed of light was made by Ole Rømer in 1670, by observation of the periods of one of Jupiter's moons. Since then it's been refined by centuries of experimentation. Michelson's 1926 experiment determining the speed of light between Mount Wilson and Lookout Mountain was probably the original basis for the value we use today, but it took until 1983 until the current standard was adopted.

So what? The invariant speed is the scale factor between time and length units. How long it took us to measure this is irrelevant.

I don't actually want to do anything. I am simply saying that if the value of the speed of light - or indeed the fine-structure constant, or anything else - were different outside the observable universe, we'd have no way of gathering any evidence.

Are you basically complaining that popularisations of cosmology don't always distinguish clearly between our models (which make falsifiable predictions about the observable universe and also make non-falsifiable predictions about areas outside the observable universe) and the reality (which may not even exist outside the observable universe)? If so, it's a fair point. I'll just observe that striking the balance between "enough detail" and "not swamping lay readers in pedantry" is tough, and very much an individual taste.

 

[Orodruin]

You're getting it back to front. The units we use now were conveniently chosen so that they more or less correspond to the ones that were used previously.

I would say you are completely missing the point with this comment. The historical ordering is obvious.

Edit: I see @Ibix has already written two well formulated posts on this theme. Two likes that would be more if I could.

 

[Vanadium 50]

Guy, are you here to

1. Learn something
2. Teach something
3. Or just to argue

I'd like to know which in order to better craft my next message

 

[GuyBarry]

Guy, are you here to

1. Learn something
2. Teach something
3. Or just to argue

All three. :-)

No, I'm just being flippant. It's a really interesting discussion but I'm too tired to contribute any more at the moment. Thanks to everyone who's taken part.

 

[PeterDonis]

It's a really interesting discussion but I'm too tired to contribute any more at the moment. Thanks to everyone who's taken part.

And with that, this thread can be closed.