What Determines the Constant Speed of Light?

[turin]

It seems ... that, according to GR, a photon's momentum can be altered by a G field perpendicular to its path but not by one parallel to it.

The proper momentum of a photon does not change in GR. One can infer, however, that the coordinate momentum of a photon changes by deflection in the first case and by red/blue shift in the latter case. Neither one of these indicates a change in velocity, since velocity and momentum aren't so intimitely related as they are in Newtonian mechanics.

I'm leaning towards the speed of the light attaining a value of c at the point of measurement regardless of the frame, but I haven't had time to get to the thought experiment proposed by Janitor.

 

[russ_watters]

I see no waffling in this statement:

Neither do I, its quite explicit: it says SR doesn't apply in non-inertial frames of reference. Its a re-statement of the domain of SR. That's not a surprise, not a shortcoming of SR, and not a statement against the constancy of the speed of light.

Integral's quote is equally clear. I don't see a problem here.

 

[russ_watters]

But back on the topic to which this thread has drifted. It seems to me what you're saying implies that, according to GR, a photon's momentum can be altered by a G field perpendicular to its path but not by one parallel to it. That seems very strange to me, but maybe you're right, or maybe that's not what you're saying.

A photon's momentum is altered by gravity in either direction. That does not, however, imply a change in speed because it is not a classical phenomenon.

 

[DrMatrix]

OK. Please reconcile the following with Integral's assertion that: "Consider this. In reality the Earth is a constantly accelerating reference frame, we measure the speed of light to be constant."

In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalization is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers.

I know how amused everyone was when I said it, so for your amusement I quote:

At the 1983 Conference Generale des Poids et Mesures the following SI (Systeme International) definition of the metre was adopted:

The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.​

This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is c constant": Yes, c is constant by definition!

In post #97, chroot said that I forgot about time dialation. I am waiting for an answer to how can I account for time dilation when I have only one reference frame.

 

[chroot]

You don't have just one. You have many, at different depths in the gravity well. Ever heard of gravitational time dilation?

- Warren

 

[DrMatrix]

You don't have just one. You have many, at different depths in the gravity well. Ever heard of gravitational time dilation?

Sure, I've heard of gravitational time dialation. Clocks deeper in a gravity well tick more slowly than a similar clock not so deep. Each clock has it's own reference frame with its own time axis. These we can compare. In the illustration, there is only one time axis. We have the path of a photon in a single reference frame. The slope of the photon changes. If the slope of the path in a space time diagram is not proportional to the speed (as I thought), what does the slope tell us?

 

[turin]

A rocket is floating out in interstellar space. A laser is floating next to the rocket. On the outside of the rocket there is some device that measures the speed of light.
...
The astronaut hits the button to fire the engine, and away he goes.
...
The laser continues to shine at the rocket. The astronaut takes readings of the speed of the laser light as calculated by the apparatus on the side of his rocket.

I have examined this thought experiment in 1+1 D Kruskal space. For those of you who don't know, this space maps the rocket frame to a 90^o wedge during the acceleration phase. The wedge border is a light cone that essentially designates an event horizon. Any light signal on the other side of the cone is causally disconnected from the 90^o wedge accelerated frame. There is a subtle (and probably unexpected to most people) consequence of this space: acceleration is a function of proper distance from the event horizon. The acceleration, a, of the rocket corresponds to a particular proper distance, ds, from the horizon as: a = c² / (-ds). For instance, assuming 10 g acceleration would put the rocket at ~0.1 ly from the horizon. I will assume a measurement device as I have described:

I will assume for my investigation that it has two points of detection (or possible four in the shape of a pyramid) separated by a known distance, and that it compares the detection times on clocks at each detection point by translating the clocks under negligible acceleration to a midpoint, and then adjusting for any time difference that appear among the clocks.

Assuming that the characteristic size of the measuring device is << the proper distance from the horizon, the measurement will be ~c, but just slightly less. This anomoly is, however, an artifact of the measurement process that I examined (specifically, the finite size of the detector), as the region surrounding any given point (event) in the accelerated frame can be transformed to an inertial region. I used a greatly exagerated detector size even for an extremely liberal acceleration (in other words, my detector size was 50% of the proper distance to the horizon), and I got c' ~ 0.8 c. Using reasonable numbers should result in c' = 0.999... c. Again, I want to emphasise that the difference in c' and c is strictly an artifact of the measurement process.

 

[DrMatrix]

from The Universe in a Nutshell by Stephen Hawking, p. 115

When the star reaches a certain critical radius, the path will be vertical in the diagram, which means that the light will hover at a constant distance from the center of the star, never getting away.

Now, I know Integral has said that resorting to a black hole means that the point is lost. But Black Holes are a well established consequence of the General Theory of Relativity -- We're not talking fringe science. And it's not like I'm asking anyone to take my word here.

I'll also note that the light at the event horizon is not orbiting. Light orbits further out -- If I'm not mistaken, at 1.5 times the critical radius.

 

[chroot]

Yes, light orbits a black hole at

$$r = \frac{3 G M}{c^2}$$

What's your point?

- Warren

 

[DrMatrix]

The point is that since light at the event horizon remains a constant distance from the star, it therefore has zero velocity, zero speed. Since zero does not equal c, the speed of light there is not c. Sorry if I wasn't clear. Does it make sense now?

 

[chroot]

The light is still moving at c -- just around in a circle. Do horses going around a racetrack also have zero velocity and zero speed?

- Warren

 

[Integral]

What has this got to do with the reasons behind a constant c?

 

[DrMatrix]

chroot,

Please re-read my post. I'm talking about light at the event horizon -- not light orbiting. The only reason I mentioned the radius where light orbited, was to avoid someone suggesting that the light at the horizon was going around in a circle. The light at the event horizon is not orbiting. It is not going around in a circle. You yourself pointed out that the radius where light orbits is further out.

The light is at a constant distance from the center and it is not going around in a circle. Zero velocity, zero speed.

To answer your question. No horses don't have zero velocity or zero speed, going around a race track.

Integral,

c is constant. The speed of light in GR is not necessarily c. You have insisted that the speed of light is constant in GR. It is not.

 

[chroot]

Right, to an outside observer, it takes anything an infinite time to cross the event horizon. Again, what's your point?

You're apparently worrying about what people see from a distance. The speed of light is c only locally.

- Warren

 

[DrMatrix]

If by locally, you mean in an inertial reference frame where one can apply SR, then you are correct. I'm sure we're all in agreement that the speed (and the velocity) of light is constant in SR and the speed equals c.

Gravity and acceleration can affect the speed and the velocity of light. Light in a non-inertial reference frame does not, in general, travel at c. For example, at an event horizon the speed is zero.

My point is that the speed of light is not necessarily c in general relativity.

 

[chroot]

Listen, DrMatrix. You've gone on and on for pages now, seemingly convinced that you're teaching us something. You're not. Many of us know a lot more about GR than you do. We all know that it takes an infinite time for anything (even light) to cross an event horizon, as seen by an outside observer. We all know that light orbits at 1.5 times the Schwarzschild radius. Duh.

Now, realize this: when someone says the speed of light is a constant, c they mean the speed of light, when passing through my measurement aparatus, is a constant, c. Physicists don't deal much with things they can't measure, and measurement is synonymous with reality for us.

You can't measure the speed of light at an event horizon. Why not? Because time stops there. You can take an apparatus down there to the event horizon, and measure light there. It doesn't even matter if the apparatus works or not, because you won't ever be able to communicate any results to anyone outside. Time has stopped for you. You are in a singular environment. If either you can't make the measurement, or you can't tell anyone else what the result of that measurement was, the measurement is moot. It doesn't matter to any of us.

No one cares about someone saying "well, from my perspective, over here, it looks like light over there is not going c!" because that is not how we define measurements, and that is not what "light always goes c" means.

You're arguing semantics. No one cares.

- Warren

 

[Integral]

Dr Matrix,

If that were the case then would we not observe the variance of c? We do not live in flat space. Space around us is curved as described by GR. The fact is we DO NOT LIVE in the idealized world of SR, yet we measure a constant c. If what you say was true, then there would be no such thing as a constant c. It would not be predicted theoretically nor observed experimentally.

While not every photon which enters a black hole ends up orbiting, it is a possible path. Most of the analysis I have seen has dealt with photons ENTERING a BH, I am not certain how we can meaningfully speak of photon which originate inside the BH? What physics do we have which allows this? Since I do not have your source in front of me (Nutshell has not made it to our pathetic library yet!) I really am uncomfortable drawing any conclusions.

I will say that I am uncomfortable with discontinuous geodesics. That is what you are describing,can a photon reach the end of a geodesic? Not at all clear to me. Consider that over time photons would accumulate at this point, what does this imply for conservation of energy?

Lots of questions, few meaningful answers.

Chroot, do you suppose I should take the time to sort some of these GR questions to a separate thread and move it to the GR forum, perhaps Nedrid can provide better answers.

 

[DrMatrix]

Physicists don't deal much with things they can't measure, and measurement is synonymous with reality for us.

You can't measure the event horizon. You certainly can't measure the singularity. Are you trying to say they are not real to you? The question of the existence of non-observables is getting away from science and into philosophy though. And I'm not sure we want to go there.

The event horizon is just the extreme where gravity causes light to stop. Gravity (acceleration) affects the speed of light and this can be measured (Although not, as you pointed out, at the horizon). John Baez said: "f you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c." There is your measurable.

Integral,

Of course, I understand your reluctance to draw conclusions based upon my quotes without the source to give you proper context. (You could ask the librarian about a inter-branch or inter-library loan. I've had to do that here. Don't get me started!)

I don't think photons accumulate at the horizon. Hovering is unstable (not sure about this though).

 

[DrMatrix]

If that were the case then would we not observe the variance of c? We do not live in flat space. Space around us is curved as described by GR. The fact is we DO NOT LIVE in the idealized world of SR, yet we measure a constant c. If what you say was true, then there would be no such thing as a constant c. It would not be predicted theoretically nor observed experimentally.

I'm not ignoring this. You make an excellent point here. I don't have the answer. [wild guess] Perhaps the gravity's effect is within the margin for error. [/wild guess]

 

[Integral]

Einstein was able to predict and Eddingion was able to measure the angle of deflection of light passing near the sun, why do we not have any predictions for the variation of the speed of light under any circumstances?

Why is it that Joao Miguliao (sp) (The Oxford physicist who has proposed the VSL theories) had colleagues who did not want to be associated with the VSL theories in spite of hours of hard work? A Variable speed of light is simply not part of accepted modern physical theory. The people who have proposed the theories have had a very hard time getting their work published in refereed journals simply because such considerations are in the realm of crackpots and not considered serious physics.

There is an effort being made to explore the implications of a Variable speed of light. I referred you to a lay person presentation of this work up thread. If you search on the correct spelling of the Joao Migualio you should be able to find more information.

 

[David]

why do we not have any predictions for the variation of the speed of light under any circumstances?

Shapiro showed that the speed of light slows down when it passes through the strong gravity field near the sun.

The trick to the “speed of light” measurement thing is that the oscillation rates of atoms slow down where light speed slows down, so atomic clocks slow down where light speed slows down, so the clocks always “measure” the speed of light to be “c” at themselves. But the actual speed of light through space in general does change as it passes in and out of strong gravity fields. This is the basic principle explained in Einstein’s 1911 gravitational redshift theory, which eventually became part of the GR theory.

 

[Integral]

Shapiro showed that the speed of light slows down when it passes through the strong gravity field near the sun.

The trick to the “speed of light” measurement thing is that the oscillation rates of atoms slow down where light speed slows down, so atomic clocks slow down where light speed slows down, so the clocks always “measure” the speed of light to be “c” at themselves. But the actual speed of light through space in general does change as it passes in and out of strong gravity fields. This is the basic principle explained in Einstein’s 1911 gravitational redshift theory, which eventually became part of the GR theory.

We have been here already. Einstein says, and means Velocity, the direction of light changes in gravitiational fields. The speed does not.

 

[David]

The speed of light was first recognized as a constant by Clerk Maxwell after he cast the fundamental equations of electromagnetism in the form of a wave equation. The term

$$\frac 1 { \sqrt {\epsilon_0 \mu_0}}$$

appeared as the propogation speed of electromagnetic waves. When he computed this constant the value was the same as the then experimental value for the speed of light.

Where were those electrodynamics experiments of the 19th Century conducted? On the surface of the earth. Thus, Maxwell’s equations tend to be a little geocentrically oriented.

 

[Integral]

There is other, more universal, evidence of the constancy of c.

 

[David]

Einstein says,

Shapiro measured it and said the return signals were delayed because they slowed down when they passed the sun. This is the 21st Century. It’s time to move ahead and not get stuck in the past. Anyway, in the 1911 theory, Einstein used c1 and c2 for the two different speeds of light passing near the sun, at different distances from the sun’s center.

 

[David]

There is other, more universal, evidence of the constancy of c.

The speed of light can’t be always “constant” everywhere relative to all systems. That’s impossible, just as the speed of sound can’t always be “constant” everywhere relative to all systems. You are just going to have to realize some day that the original 1905 constancy postulate was just flat out wrong.

Remember, it was proposed in the days when Einstein thought the fastest objects moving in the universe were the planets, he thought the stars were “fixed”, he didn’t know the universe was expanding, and that was before he realized that strong gravity fields slow down the speed of light. He didn’t figure that out until 1911.

When the Earth is moving toward a star that is fixed relative to the sun, we see a blueshift in the star’s light, and we see a redshift in the light coming from stars that are in the opposite direction. That indicates that the speed of light is controlled in our solar system by something inside the space of our solar system, and it indicates that we are moving toward the blueshifted light at the additive velocity of c + v and the redshifted light is moving toward us at the subtractive velocity of c – v, with v being our speed around the sun.

If you study the Doppler Effects, you will find that Doppler predicted this redshift and blueshift in 1843, and you will also learn that there are two main causes for these kinds of redshifts and blueshifts. One is a physical lengthening and shortening of waves (wavelengths) in space, and the other is caused by a less rapid and more rapid encountering of the waves. Study the Doppler Effects regarding sound and you’ll see what I’m talking about.

The redshifts and blueshifts due to the earth’s motion around the sun are due to subtractive and additive light-speed effects. This is common Doppler theory, it was well thought-out, explained, and predicted more than 160 years ago. When spectroscopes were adapted to telescopes, they proved the classical Doppler theory to be correct.

 

[David]

There is other

Here, read Dr. Su’s paper, “Quantum Electromagnetics – A Local-Ether Wave Equation Unifying Quantum Mechanics, Electromagnetics, and Gravitation,” and he’ll explain the whole thing to you. His papers are all over the internet and have been published in several languages and in several mainstream physics journals in several countries. This is not called “relativity” anymore. It’s called “quantum mechanics” and “electromagnetics”. “Relativity” is sort of an old-fashioned term now.

http://qem.ee.nthu.edu.tw/outline.pdf

 

[chroot]

Enough psuedoscience and handwaving. The original question has been answered in sufficient detail. David, keep your personal ideas out of the General Physics forum.

- Warren