Speed of Light Puzzle: Is c a Localized Value?

[GuyBarry]

Hello - I'm posting this here because of a discussion I got into on another forum following the recent death of Stephen Hawking. I should stress that I am by no stretch of the imagination a physicist (though I did do modules on special relativity and quantum mechanics as part of my maths degree 30 years ago, most of which I've forgotten).

I'd like to know this. We're told that the speed of light is a fundamental constant of nature. We're told that the universe is about 13.8 billion years old. We're told that, as a consequence, it is physically impossible to observe any signal further away from us than light can travel in 13.8 billion years (which turns out not to be 13.8 billion light-years as I always thought, but 46.5 billion light-years, because the universe has expanded since the signal was emitted). All of this I accept.

We also have no reliable way of estimating the size of the universe, as I understand it. It may be orders of magnitude larger than the observable universe, or even infinite.

So how do we know that the speed of light is constant throughout the universe? If the observable universe is in reality a tiny - maybe infinitesimal - region within the greater universe, then it's entirely possible that c = 299,792,458 m/s may in reality be a localized value within that region. And because it's impossible to observe any signal from beyond that region, it's impossible to collect any data that would provide evidence otherwise.

This has been puzzling me a great deal, so I'd appreciate any enlightenment on the issue.

 

[Drakkith]

So how do we know that the speed of light is constant throughout the universe?

We don't. But we can say that it must be equal to c to within a very, very tiny margin of error for the observable universe because of how c is related to other fundamental constants and concepts. We usually choose to believe this to be the case for the rest of the universe because of the belief that the laws of physics don't change when we move to a different point in the universe. It may be the case that the laws of physics do change when we've gone far enough away, but that the distance required to observe any change lies well outside the observable universe.

 

[GuyBarry]

We don't. But we can say that it must be equal to c to within a very, very tiny margin of error for the observable universe because of how c is related to other fundamental constants and concepts. We usually choose to believe this to be the case for the rest of the universe because of the belief that the laws of physics don't change when we move to a different point in the universe. It may be the case that the laws of physics do change when we've gone far enough away, but that the distance required to observe any change lies well outside the observable universe.

Since either possibility is consistent with all the observable data, what grounds are there for choosing the first over the second?

 

[.Scott]

A speed of light is built into the structure of the universe. And if it's different somewhere else, then all of the chemistry is changing in a proportional manner. When we look back at light that is 12 billion years old and from 12 billion years away, we see a red-shifted version of the same spectrum patterns that are generated in our own solar system. The chemistry isn't different.

So the speed of light relative to common objects is also likely to be the same. If you moved a meter stick and a stop-watch to another part of the universe, you would get the same measured speed of light. Either because it is the same, or because the chemistry in those objects changed proportionately.

 

[Orodruin]

It should be mentioned that, as a quantity with dimension, the speed of light is utterly dependent on the units being used. In relativity, it is an intrinsic property of space-time and as such it is not possible to have it vary as it is a conversion factor between units of length and units of time. Using a different speed of light would just change the unit of time or the unit of length. Having a different speed of light is therefore not typically something one would consider when one considers the possibility of different natural constants in different parts of the Universe.

 

[GuyBarry]

But is it possible that the constant value c, which is intrinsic to the theory of relativity as the conversion factor between length and time, is not in fact equal to the speed of light in all parts of the Universe?

I'm thinking of a historical analogy from the time that the period of rotation of the Earth was assumed to be constant, and used for the basis of the measurement of time. We now know this not to be the case, and use a different basis for the measurement of time.

 

[Orodruin]

But is it possible that the constant value c, which is intrinsic to the theory of relativity as the conversion factor between length and time, is not in fact equal to the speed of light in all parts of the Universe?

No. Not if you want to describe it with relativity. It is just a choice of what units you use to measure lengths and what units you use to measure time. The typical thing to do in relativity is to use units such that $c = 1$.

 

[jbriggs444]

Since either possibility is consistent with all the observable data, what grounds are there for choosing the first over the second?

Occam's razor.

If the speed of light (or any particular dimensionless constant) is the same throughout the universe, that is one parameter to determine. If it varies throughout the universe, that is at least two parameters and possibly more. You would have to describe how it varies. Among theories which fit the facts, theories with fewer tuneable parameters are preferred over theories with more.

 

[itfitmewelltoo]

Hello - I'm posting this here because of a discussion I got into on another forum following the recent death of Stephen Hawking. I should stress that I am by no stretch of the imagination a physicist (though I did do modules on special relativity and quantum mechanics as part of my maths degree 30 years ago, most of which I've forgotten).

I'd like to know this. We're told that the speed of light is a fundamental constant of nature. We're told that the universe is about 13.8 billion years old. We're told that, as a consequence, it is physically impossible to observe any signal further away from us than light can travel in 13.8 billion years (which turns out not to be 13.8 billion light-years as I always thought, but 46.5 billion light-years, because the universe has expanded since the signal was emitted). All of this I accept.

We also have no reliable way of estimating the size of the universe, as I understand it. It may be orders of magnitude larger than the observable universe, or even infinite.

So how do we know that the speed of light is constant throughout the universe? If the observable universe is in reality a tiny - maybe infinitesimal - region within the greater universe, then it's entirely possible that c = 299,792,458 m/s may in reality be a localized value within that region. And because it's impossible to observe any signal from beyond that region, it's impossible to collect any data that would provide evidence otherwise.

This has been puzzling me a great deal, so I'd appreciate any enlightenment on the issue.

There is an existing theory that considers exactly this, that the speed of light may not have been 3x10^8 but that it may have varied. It is the work of a couple of theoretical physisists.

 

[itfitmewelltoo]

Hello - I'm posting this here because of a discussion I got into on another forum following the recent death of Stephen Hawking. I should stress that I am by no stretch of the imagination a physicist (though I did do modules on special relativity and quantum mechanics as part of my maths degree 30 years ago, most of which I've forgotten).

I'd like to know this. We're told that the speed of light is a fundamental constant of nature. We're told that the universe is about 13.8 billion years old. We're told that, as a consequence, it is physically impossible to observe any signal further away from us than light can travel in 13.8 billion years (which turns out not to be 13.8 billion light-years as I always thought, but 46.5 billion light-years, because the universe has expanded since the signal was emitted). All of this I accept.

We also have no reliable way of estimating the size of the universe, as I understand it. It may be orders of magnitude larger than the observable universe, or even infinite.

So how do we know that the speed of light is constant throughout the universe? If the observable universe is in reality a tiny - maybe infinitesimal - region within the greater universe, then it's entirely possible that c = 299,792,458 m/s may in reality be a localized value within that region. And because it's impossible to observe any signal from beyond that region, it's impossible to collect any data that would provide evidence otherwise.

This has been puzzling me a great deal, so I'd appreciate any enlightenment on the issue.

VSL,
https://www.theguardian.com/science...s-view-on-speed-of-light-could-soon-be-tested

 

[GuyBarry]

That's very interesting - thanks.

Magueijo and Afshordi’s theory does away with inflation and replaces it with a variable speed of light. According to their calculations, the heat of universe in its first moments was so intense that light and other particles moved at infinite speed. Under these conditions, light reached the most distant pockets of the universe and made it look as uniform as we see it today.

Does that mean that they presume that the theory of relativity didn't hold in the early moments of the universe?

 

[PeroK]

That's very interesting - thanks.

Does that mean that they presume that the theory of relativity didn't hold in the early moments of the universe?

That Guardian article is not a valid source of scientific results or theories. It's sensationalist garbage, which has no bearing on the actual science.

For example:

"... propose that light tore along at infinite speed at the birth of the universe ..."

Infinite speed doesn't represent motion in any sense. It's impossible to know what they mean by that.

Moreover, the theory of SR postulates that the speed of light is invariant (between inertial reference frames). Not "constant". That there is a subtle but significant difference emphaises the gulf between the Guardian and a reputable scientific text.

 

[russ_watters]

Occam's razor.

If the speed of light (or any particular dimensionless constant) is the same throughout the universe, that is one parameter to determine. If it varies throughout the universe, that is at least two parameters and possibly more. You would have to describe how it varies. Among theories which fit the facts, theories with fewer tuneable parameters are preferred over theories with more.

...and since we'll never know and it has no impact on our theories, one could assume literally anything about the universe outside our visible chunk. Such assumptions could even be considered a step worse than an Occam's razor test. Generally, Occam's razor is used to judge a theory that needs extra assumptions to make it work vs one that doesn't. In this case the extra assumptions aren't even needed, but it is being suggested we add them in anyway.

 

[GuyBarry]

...and since we'll never know and it has no impact on our theories, one could assume literally anything about the universe outside our visible chunk.

So essentially, if I've understood correctly, the answer to my original question is "We don't know that the speed of light isn't constant outside the observable universe, but since it doesn't affect any of our theories about the observable universe it doesn't matter".

If I were to propose "the laws of physics as we understand them hold up to the boundaries of the observable universe, and everything beyond that is made of cheese", would there be any way of falsifying it?

 

[Orodruin]

If I were to propose "the laws of physics as we understand them hold up to the boundaries of the observable universe, and everything beyond that is made of cheese", would there be any way of falsifying it?

Of course not - by definition of "observable universe". Therefore, it also does not make for a very good physics theory.

 

[PeroK]

So essentially, if I've understood correctly, the answer to my original question is "We don't know that the speed of light isn't constant outside the observable universe, but since it doesn't affect any of our theories about the observable universe it doesn't matter".

If I were to propose "the laws of physics as we understand them hold up to the boundaries of the observable universe, and everything beyond that is made of cheese", would there be any way of falsifying it?

I think such questions are unscientific. Any theory must have a justification: What are you trying to explain with your cheese proposition?

 

[GuyBarry]

As I thought. So really, when I hear cosmologists talking about "the universe", they're really only talking about "the observable universe". They can't possibly have any coherent theories of the rest of it.

I don't think I'd really appreciated that up until now.

 

[jbriggs444]

As I thought. So really, when I hear cosmologists talking about "the universe", they're really only talking about "the observable universe". They can't possibly have any coherent theories of the rest of it.

Consider that we have a theory that entails that the sun will come up on April 5. As I write this, that prediction of the theory has never been tested. Nonetheless, the theory is coherent. Its predictions for past sunrises have been tested and found to be accurate. We have no good reason to doubt that its prediction for April 5 will be as accurate as its prediction for April 4.

 

[russ_watters]

As I thought. So really, when I hear cosmologists talking about "the universe", they're really only talking about "the observable universe". They can't possibly have any coherent theories of the rest of it.

That's the inverse of what you just said before and it is most certainly *not* true. The fact that it makes no sense to assume the rest of the universe is different does not mean it also doesn't make sense to assume it is the same. It makes much more sense to assume it is the same.

 

[GuyBarry]

That's not how I see it. It makes no sense to assume it is different, and it makes no sense to assume it is the same. It makes no sense to assume anything at all, because there's no data. The best that anyone can say is "this is what we know about the observable universe, and the rest we can't know".

 

[jbriggs444]

That's not how I see it. It makes no sense to assume it is different, and it makes no sense to assume it is the same. It makes no sense to assume anything at all, because there's no data. The best that anyone can say is "this is what we know about the observable universe, and the rest we can't know".

And yet we plan for the sun to come up tomorrow.

 

[GuyBarry]

Consider that we have a theory that entails that the sun will come up on April 5. As I write this, that prediction of the theory has never been tested. Nonetheless, the theory is coherent. Its predictions for past sunrises have been tested and found to be accurate. We have no good reason to doubt that its prediction for April 5 will be as accurate as its prediction for April 4.

But we can test that prediction. We can't test any predictions about anything outside the observable universe.

 

[jbriggs444]

But we can test that prediction. We can't test any predictions about anything outside the observable universe.

We can never test the prediction that the sun will come up tomorrow. Tomorrow is always a day away.

 

[GuyBarry]

Isn't it quite a simple logical argument?

(1) Scientific theories are required to be falsifiable.
(2) Any theory of anything beyond the observable universe is, by definition, not falsifiable.
(3) Therefore any theory of anything beyond the observable universe is unscientific.

 

[jbriggs444]

Isn't it quite a simple logical argument?

(1) Scientific theories are required to be falsifiable.
(2) Any theory of anything beyond the observable universe is, by definition, not falsifiable.
(3) Therefore any theory of anything beyond the observable universe is unscientific.

Sure. But you did not say "unscientific" previously. You said "incoherent". Those are two entirely different characterizations.

 

[GuyBarry]

OK, I concede that. It's certainly possible to put togther a coherent theory of the unobservable universe - just not one that can be scientifically tested.

And if it's not within the realm of science, why are cosmologists trying to do it?

 

[jbriggs444]

OK, I concede that. It's certainly possible to put togther a coherent theory of the unobservable universe - just not one that can be scientifically tested.

And if it's not within the realm of science, why are cosmologists trying to do it?

They are trying to explain the observations from the observable universe and make predictions that can be tested within the observable universe. But having a theory with an unexplained boundary at the edge of what is observable Mars the coherence of the theory. So instead of coming up with a theory with a cut-off on the edge, one comes up with a theory without a cut-off.

 

[GuyBarry]

That's fair enough I suppose, but it's not a scientific theory. It's a plausible hypothesis based on the Occam's razor principle, as mentioned earlier. I agree that it would be highly unlikely if the laws of physics suddenly changed at the boundaries of the portion of the universe observable from Earth - that would be taking geocentrism to new heights!

But it's perfectly possible that the Earth happens to be located in a region of the universe where c = 299,792,458 m/s and all those other fundamental physical laws happen to be valid, for reasons we can't know. It may extend well beyond the boundaries of the observable universe. And any speculation about this is outside the realm of science.

 

[Vanadium 50]

t the sun will come up tomorrow. Tomorrow is always a day away.

Channeling Martin Chamin?

The sun'll come out
Tomorrow
Bet your bottom dollar
That tomorrow
There'll be sun
...
Tomorrow, tomorrow
I love you tomorrow
You're always
A day
Away

That's fair enough I suppose, but it's not a scientific theory.

That's not how science is done, I'm afraid. Science is also about inference. The fact that I have measured the mass of a million carbon atoms and always gets me the same result allows me to infer the mass of a carbon atom which is not in the process of being measured,

 

[GuyBarry]

The fact that I have measured the mass of a million carbon atoms and always gets me the same result allows me to infer the mass of a carbon atom which is not in the process of being measured,

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, because the very fact of the constant value of the speed of light within the observable universe prevents us from getting data about the unobservable universe. So you can't draw any conclusions about the unobservable universe based on it.

 

[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?