Speed of light or Speed limit of Spacetime?

[ebos]

I'm having a difficult time researching the answer to my question about the speed of light. Now obviously it is a speed not only reserved for light but also all other massless particles/waves. It's obviously a constant property of our Spacetime since we can manipulate th speeds of different massless particles but we cannot manipulate any to travel faster than 'c'.
So I've been wondering, for example if the M-M experiment and all subsequent experiments to measure the speed of light had failed (perhaps our instruments weren't sensitive enough yet), would we still somehow be able to come up a with an alternate method to predict 'c' without measuring the speed of anything.

 

[rootone]

Do you mean that the idea of there being a luminiferous aether might have been right all along, but the MM experiments were not sufficiently sensitive?
I think there were subsequent more sensitive experiments, but nothing different happened.
Anyway Einstiens relativity theories then came along explaining light propagation without need for luminiferous aether

 

[Mister T]

As far as I know, it's the classical relationship between electric and magnetic fields that predicts the speed of light. This was first accomplished by Maxwell in the 1860's, but Einstein's 1905 theory of relativity shed further light on that relationship.

The speed c is a speed that's both the same for all observers (invariant) and the ultimate speed. Even if it were discovered that light travels at a speed that's less than c, nothing in the equations would need to be modified. We would simply refer to c as the ultimate speed, or equivalently the invariant speed, rather than the speed of light.

 

[PeterDonis]

if the M-M experiment and all subsequent experiments to measure the speed of light had failed

The Michelson-Morley experiment didn't measure the speed of light; it measured whether the speed of light changed depending on the measuring device's state of motion. It did not give an actual value for the speed of light; it could only give a result of either "change observed" or "no change observed".

I'm not sure what other experiments you are referring to.

we can manipulate th speeds of different massless particles

Not really. When light travels through a material medium, it appears to move slower than $c$, yes. But when you actually dig into what's going on, you find that it isn't that we actually manipulate the speed of any massless particle (the photon, in the case of light). What we do can be viewed as either making photons behave as if they had mass, or as the atoms in the medium absorbing photons and re-emitting them after some time delay, so the net effect is to make the light seem to be moving slower even though the actual massless particles, the photons, are still traveling at $c$ in between absorptions and re-emissions.

 

[PeterDonis]

As far as I know, it's the classical relationship between electric and magnetic fields that predicts the speed of light.

Maxwell electrodynamics predicts that electromagnetic waves will travel with a certain speed that is invariant under Lorentz transformations, yes. But that's not quite the same as showing that that invariant speed is a fundamental property of spacetime.

The speed c is a speed that's both the same for all observers (invariant) and the ultimate speed.

It is also the speed at which all massless particles must travel--or, to put it another way, it is the speed at which all objects with null 4-momentum vectors must travel. The latter property is the one that links up this "speed" with a fundamental property of spacetime--namely, the null cones, which are invariant geometric features of spacetime.

 

[ebos]

OK let's say you can measure the speed of the world's fastest car You'd probably use a high-tech speed register like a radar gun or something equivalent. Or some old die-hards could use clocks and metre sticks. But let's say in measuring things we were really backward but in engineering stuff we were the best (never mind thee approaching contradiction). Could not the engineers figure out the top speed of the car using friction, road surface. temperature that day, orbit of the car as it went around the track, horsepower of the engine minus the friction of everything else, etc etc. ? Wouldn't they still be able to figure out a top speed w/o actually measuring the top speed. All the stuff you guys have given me are not helping because you're straying from my though experiment scenario. Without measuring the speed of light OR perhaps we were still not even considering measuring the speed of light because we had none of the necessary instruments, couldn't they still take all the other factors in play and forecast a maximum speed that the universe would allow? Remember, no measuring of fast things... or histories at past attempts at measuring the speed of light. That's just redundancy. I read one article once that was going there and somehow lost it and have not been able to find it again.

 

[PeterDonis]

Without measuring the speed of light OR perhaps we were still not even considering measuring the speed of light because we had none of the necessary instruments, couldn't they still take all the other factors in play and forecast a maximum speed that the universe would allow?

You can predict from Maxwell's Equations, i.e., from observations of electrodynamics that don't involve anything moving very fast, that electromagnetic waves should exist and should travel at a very fast speed that is invariant under Lorentz transformations. But the only way to confirm that prediction was correct would be to measure the speed of electromagnetic waves.

It would seem that similar remarks would apply to any other indirect way of trying to figure out a maximum speed. You could make predictions based on indirect evidence, but how would you know the predictions were correct except by actually measuring the speeds of very fast objects?

 

[rootone]

It's not difficult to demonstrate the speed of light.
In fact we need to assume that it is a constant as Einstein proposed and is what it is observed to be,
Otherwise communicating with spacecraft , even those not so far from Earth, would be unreliable.

 

[PeterDonis]

In fact we need to assume that it is a constant as Einstein proposed and is what it is observed to be,
Otherwise communicating with spacecraft , even those not so far from Earth, would be unreliable.

Careful. In a curved spacetime, the issue of the "speed" of light is not so simple. In general, the coordinate speed of light in a curved spacetime is not constant; in fact, coordinates that are commonly used for tracking spacecraft have this property. The variation in the coordinate speed of light in these coordinates is not large, but it is not necessarily negligible either.

In curved spacetime, the rule that corresponds to "constant speed of light" in flat spacetime, i.e., in SR, is that the worldlines of objects must be inside the light cones at every event.

 

[robphy]

If you had access to high-precision clocks that moved at terrestrial speeds,
you would see that,
on a spacetime diagram, the curve of "constant-time-interval" from an event
would not lie on a line... but on a hyperbola.
By boldly extrapolating, one could determine the asymptotes of the hyperbola,
corresponding to the speed of light [or arguably more correctly the maximum speed of signal propagation].


(Added in edit:
Note that we (as Galileans) have boldly extrapolated from our not-very-precise clocks to claim that the curve of "constant-time-interval" from an event DOES lie along a line... Implying an infinite maximum speed of signal propagation. However, improved measurements suggest that this conclusion is incorrect.)

 

[ebos]

OK. One more time. Did anyone know the speed 'c' by calculations before anyone else measured the speed of 'c' with instruments? As in, did the measurement of light speed fulfill an older prediction made by an older smarter person?

 

[PeterDonis]

Did anyone know the speed 'c' by calculations before anyone else measured the speed of 'c' with instruments?

As things worked out historically, no; the speed of light was measured (with rather poor accuracy at first) well before anyone had any theoretical reason to expect it to have any particular value.

There's no particular reason, though, why things couldn't have worked out differently--why, for example, electrodynamics couldn't have progressed to the point of making a prediction about the speed of light before the speed of light was actually measured. It just didn't happen to work out that way in our actual history.

 

[Ibix]

For example, this paper:
http://arxiv.org/abs/1005.2062
derives the Lorentz transforms using only theoretical considerations and maths that were available to Newton. It never occurred to anybody to approach the problem that way, but the tools were available - or so the author says. I don't know enough about the history of maths to comment.

 

[PAllen]

In principle, if absurdly precise measurements were made of the result to shooting bullets from a highly calibrated, consistent, gun, from a very fast race car, at different speeds, u, of the race car (and different bullet speeds, v, of the gun) you could explore the relation between the bullets progress relative to the ground (factoring in air resistance with very high precision) compared to the sum of the car speed and the speed of the bullet relative to the gun. You could arrive at the fact that bullet speed relative to the ground is not u + v but:

(u+v)/(1+ u*v/c²)

where c is a mysterious constant. The above algebra leads to the feature that no matter how many times you add a speed < c to another speed < c, the result is always still < c. This would suggest this mysterious constant is a fundamental speed limit. Note that none of the speeds need be close to c given arbitrarily accurate precision.

In a sense, this is the speed analog of Robphy's moving clock suggestion. His gets first the relativistic affect on time. The above gets first the fundamental speed limit feature.

But, as others have said, there is no evidence of anyone proposing a fundamental speed limit or notion spacetime before the development of special relativity (I include here the whole group working partly overlapping ways from the late 1800s to 1910).

 

[Mister T]

OK. One more time. Did anyone know the speed 'c' by calculations before anyone else measured the speed of 'c' with instruments?

In the 1860's Maxwell predicted that electromagnetic waves should propagate at a speed that he was able to calculate based only on electromagnetic interactions (for example, the strength of a magnetic field produced by a current-carrying wire). When his calculation gave him a number that matched the previously measured speed of light, he realized that he'd discovered the nature of light.

As in, did the measurement of light speed fulfill an older prediction made by an older smarter person?

No. People had been measuring the speed of light for a couple of centuries prior to that, so historically it wasn't so much a prediction of the speed that Maxwell made, but rather a prediction about the nature of light waves. It turns out that he got it right, just as it turned out that Einstein got it right a few decades later when he made predictions about the relationship between magnetic and electric fields. How they were able to get it right is a mystery. Were they smart or were they lucky? Likely it was both!

 

[Nugatory]

In principle, if absurdly precise measurements were made of the result to shooting bullets from a highly calibrated, consistent, gun, from a very fast race car, at different speeds, u, of the race car (and different bullet speeds, v, of the gun) you could [discover what we now know as relativistic velocity addition, with this mysterious constant $c$ buried in it]

Fizeau actually came close in 1850. He had an experimental setup that was sufficiently sensitive, and there was a significant difference between his measurements and the $u+v$ he and everyone else expected.

Of course no one interpreted this result as a falsification of Galilean relativity. That's to be expected; the theoretical and mathematical framework that we're drawing on in this thread didn't exist back then so there was no alternative to consider.

 

[ebos]

So I can assume that the only reason for the speed of light is the speed of light? I thought I read an article fairly recently where someone proved why light (etc.) travels at exactly the speed that it does. Is it anything to do with the density of spacetime? Or the vacuum? Sorry for being a pest but this bugs me.

 

[ebos]

By the way, forgot to mention, thanks everyone.

 

[vanhees71]

That electromagnetic waves travel at the limiting speed of a relativistic spacetime cannot be "proven" in any way, i.e., so far it cannot be explained by a deeper theoretical reason like a symmetry principle. Nothing in the current theories (particularly the Standard Model of elementary particle physics) restricts the photon mass in any way, and thus we must take it as an empirical fact that the photon mass is very small (the current limit is $m_{\gamma}<10^{-18} \text{eV}/c^2$). So far there's not the slightest hint that it is not exactly 0, and thus in the current models it's treated as an Abelian gauge boson with exactly 0 mass.