What Determines the Constant Speed of Light?

[Integral]

The conclusion is then that it is not a constant in mph which used to be a different standard from the meter?

If it is constant by the definition of the meter then perhaps it is not constant in different units which are not defined in terms of the speed of light.

If it is constant in units not defined in the terms of light then what do you mean by constant by definition of the meter?

 

[Jack Martinelli]

Jack,
The same qualifers apply to [tex]\epsilon_0[/tex] that turin stated with c up thread.

Why do you introduce QM to the question. Are you simply looking for arguments.

It's a yes or no question.

Is c constant?

Sorry. This thread is beginning to unravel & I may have misread something you (or someone else wrote).

BTW, I think I've said just about all I can about the speed of light. You're right, c is a constant. You'll get no more arguments from me.

 

[DrMatrix]

If it is constant by the definition of the meter then perhaps it is not constant in different units which are not defined in terms of the speed of light.

If it is constant in units not defined in the terms of light then what do you mean by constant by definition of the meter?

Does this explain? The speed of light is constant in meters per second because the meter is defined in terms of the speed of light. The speed of light is constant when the distance is measured by rigid rods because that's just the way the universe works. The speed of light may or may not be constant in units not defined in terms of the speed of light. The speed of light is not constant in General Relativity. So if our unit of length is based upon the coordinates of a non-inertial reference frame, the speed of light would not be constant.

 

[Loren Booda]

Are [tex]\epsilon_0[/tex] and [tex] \mu_0[/tex] invarient regardless of reference frame as c is?

 

[turin]

Are [tex]\epsilon_0[/tex] and [tex] \mu_0[/tex] invarient regardless of reference frame as c is?

It is believed to be so, in empty flat space.

 

[Integral]

The speed of light is not constant in General Relativity

This is incorrect. c is constant in the General Theory.

Looks like you have some pretty fundamental misunderstandings. It is to bad that you cannot use this site to clear up those misunderstanding rather then attempt to present your incorrect opinions as physical fact.

One more time.

c is constant in all coordinate systems. These coordinate systems can even have a constant velocity. All will agree (after unit conversions) on the speed of light.

Jack,
For all of your words, and even considering the meaning of your words you have not and cannot prove that the speed of light is constant using only sticks and clocks. At least here and in words. To accomplish this would require actual measurements, even then you have not proven the constancy of c. You have only a single value at a single location. It is impossible to generalize that single measurement to apply to all locations and times. Historically, the constancy of c was not established until the work of Maxwell. It was his work that laid the theoretical basis of the constancy of c. His work forced the world of physics to come to grips with an ugly fact. This fact, that the speed of light was determined by well known and understood fundamental constants and only those constants, had very deep implications which shook the world of physics to its very foundations. To attempt to prove the constancy of c without reference to E&M is, in my opinion, impossible.

 

[DrMatrix]

This is incorrect. c is constant in the General Theory.

Looks like you have some pretty fundamental misunderstandings. It is to bad that you cannot use this site to clear up those misunderstanding rather then attempt to present your incorrect opinions as physical fact.

One more time.

c is constant in all coordinate systems. These coordinate systems can even have a constant velocity. All will agree (after unit conversions) on the speed of light.

A beam of light trying to escape a black hole will hover at the event horizon. There you have light that is motionless. If I attach a coordinate system to the rotating earth, pluto is traveling faster than c. The speed of light is not constant in a general coordinate system.

Inertial coordinate systems can hae a constant velocity, sure. And the speed of light is constant in inertial frames, but not in general reference frames.

 

[cookiemonster]

I don't think anybody was asserting otherwise.

cookiemonster

 

[Integral]

A beam of light trying to escape a black hole will hover at the event horizon. There you have light that is motionless.

No. light follows geodesics. Inside the event horizon of a black hole geodesics form closed paths. When light enters a black hole it essentially orbits the singularity. One must be very carefully when doing physics in the vicinity of the singularity. Let us stay in our everyday universe. If you must resort to black holes to support your argument you are lost.

The speed of light is constant in GR.

 

[Janitor]

Thought experiment.

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. If the laser is pointing at this device on the rocket, the astronaut in the rocket gets a reading of precisely c on his LCD readout.

The astronaut hits the button to fire the engine, and away he goes. The laser remains behind, in free fall. 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.

The rocket runs out of fuel, and coasts at some high speed. The astronaut sees that the light from the laser is redshifted, but (I think everyone in this thread will agree) he sees precisely c on his LCD readout.

So my question is, what does the readout show for the powered phase of the rocket? I thought I had read at least once somewhere that it would read less than c. Does anyone agree? Does anyone disagree?

Or is this little thought experiment not even relevant to what you are discussing? Certainly the rocket itself can be thought of as a reference frame, one that is inertial for a time, then non-inertial for a time, then inertial once again, and we agree to ignore gravitational fields from heavenly bodies, which by assumption are all very far away.

 

[DrMatrix]

The speed of light is constant in GR.

Wrong!
From A Few Inferences from the General Theory of Relativityhttp://www.bartleby.com/173/22.html by Albert Einstein:

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.

Janitor, so long as your reference frame is inertial, you can apply Special Relativity where the speed of light is constant. In a non-inertial reference frame, the velocity of light is not constant.

 

[Integral]

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.

Velocity is a very critical word in this paragraph. Without appreciation for the precise meaning of this word, one might think that he is saying that the speed of light is changing. But he did not say speed, he said velocity, he is telling us that light does not travel in straight lines (or what we consider to be straight lines) but changes direction in a gravitational field, therefore the velocity of light must change.

This says nothing of the speed of light. The speed of light remains constant but its velocity {direction} changes in a gravitational field.

 

[jdavel]

Integral said: "The speed of light remains constant but its velocity {direction} changes in a gravitational field."

I'm going to have to be careful here, because I know virtually nothing about GR. If the g field and the direction the light travels are perpendicular, then what you said seems right, direction changes but speed stays the same. But if they're parallel, wouldn't it be the other way around?

The SR postulate of constant c is limited to measurements in inertial frames. I thought that in GR the postulate is limited to both inertial frames and zero gravity locations.

 

[turin]

quoting Integral
Quote:

The speed of light is not constant in General Relativity

This is incorrect. c is constant in the General Theory.

The speed of light in a literal sense of meaning is different than c. I can say that c is a constant everywhere in the universe, and you have shown that we agree what I would fundamentally mean by that: the constant that shows up in the wave equation that has units of speed. I can also say that the literal speed of a beam of light is different than c, both in the context of refraction, as well as in a coordinate system that considers a beam of light to hover at a horizon.

quoting DrMatrix
A beam of light trying to escape a black hole will hover at the event horizon. There you have light that is motionless. If I attach a coordinate system to the rotating earth, pluto is traveling faster than c. The speed of light is not constant in a general coordinate system.

I agree. c is a constant in that coordinate system, but it only replaces the literally speed of light locally in general, where an experiment can be done to examine Maxwell's equations.

quoting Integral
When light enters a black hole it essentially orbits the singularity.

I don't know what you mean by "enters a BH," but once anything gets "closer" to the "singularity" than a certain critical radius (I believe it is the Schwarzschild radius), orbits do not exist. The path of a photon inside a BH is a spiral that terminates at the singularity within a finite time interval in a coordinate system outside the BH, if I'm not mistaken. I guess you could mean "orbit" in the loose context of "free particle trajectory," so, I don't want to disagree with you. Is that what you mean?

quoting Integral
Let us stay in our everyday universe. If you must resort to black holes to support your argument you are lost. The speed of light is constant in GR.

Say what? Why has this arbitrary rule of not resorting to a 90 year old well established theory been introduced? And the speed of light is not necessarily constant in GR, but c is.

quoting Janitor
Thought experiment.
... there is some device that measures the speed of light.
...
So my question is, what does the readout show for the powered phase of the rocket? I thought I had read at least once somewhere that it would read less than c. Does anyone agree? Does anyone disagree?

I will have to defer this to some investigation, but I would ask how the device measures the value. I believe that the thought experiment critically depends on this. 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.

quoting Janitor
... is this little thought experiment not even relevant to what you are discussing? Certainly the rocket itself can be thought of as a reference frame, one that ... non-inertial for a time, ...

I think it's relevant. I'm with you.

 

[russ_watters]

Good luck, Integral - I'm out.

 

[DrMatrix]

When light enters a black hole it essentially orbits the singularity.

I don't know what you mean by "enters a BH," but once anything gets "closer" to the "singularity" than a certain critical radius (I believe it is the Schwarzschild radius), orbits do not exist. The path of a photon inside a BH is a spiral that terminates at the singularity within a finite time interval in a coordinate system outside the BH, if I'm not mistaken. I guess you could mean "orbit" in the loose context of "free particle trajectory," so, I don't want to disagree with you. Is that what you mean?

I was wondering what Integral meant too. Perhaps he'll explain.

In The Universe in a Nutshell by Stephen Hawking on page 114 Figure 4.12 we see a diagram of a star with rays of light leaving the surface. The axes are chosen so that a velocity of c will have slope equal to 1 or -1. The caption reads:

Spacetime around a non-collapsing star. Light rays can escape from the surface of the star (the red vertical lines). Far from the star, the light rays are at 45 degrees to the vertical, but near the star the warping of spacetime by the mass of the star causes the light rays to be at a smaller angle to the vertical.

Is the speed of light constant here? I'd say no. What say you?

 

[Integral]

Is the speed of light constant here? I'd say no. What say you?

Sure, what evidence have you provided to show otherwise?

Going to work, I drive 60Mph west, on the way home I drive 60mph East. Same speed different velocity.

What! No response to my reply to your Einstein quote? going try and simply ignore it, perhaps?? Just trot out another quote from another book that you thought you understood. Nice tactics, how to keep the argument going and convince yourself you are ahead. Ignore your failures and move on to a new and different misunderstanding.

It appears to me your understanding of basic physics is not even at the Halliday and Resnick level. (ie not able to appreciate the difference between velocity and speed, consider a square root to be a "fancy equation" )It would do you well to move beyond the coffee table physics books and attempt to learn the real deal. Start with a calculus text. Move on to a college level Physics text. Open your mind a bit, currently you are blinded by preconceived notions and crippled by your lack of formal physics knowledge.

The event horizon separates the universe from the black hole, what is different inside the event horizon? According to your man Hawking, inside the event horizon geodesics form closed paths. Thus light that enters a black hole tangent to a interior geodesic follows that path endlessly.


Hey I thought these were Hawking's ideas. You did read Brief History of time ? Perhaps I got it out of the collection of lectures by Hawking and Penrose.

If this is going to turn into a discussion of GR I will move the thread to the appropriate forum where mentors, with better knowledge of the details then I, can answer your questions.

BTW it would be nice if you could learn to ask questions to clarify your understanding.

Edit: Grammar and punctuation.

 

[Integral]

Janitor,
Consider this. In reality the Earth is a constantly accelerating reference frame, we measure the speed of light to be constant. We live deep in the suns "gravity well". this means that, according to GR, Space time is not flat in our vicinity. We still measure a constant speed of light. If you conduct your experiment deep in space away from the influence of stars and planets would not space/time be flatter there then here? We measure a constant speed of light, why would you expect anything different on your space ship?

This is not meant to be an end all answer to your question, just something to think about.

 

[DrMatrix]

Sure, what evidence have you provided to show otherwise?

The caption I quoted. It's easier to understand with the figure in front of you, but I'll try to explain. The x-axis is space and the y-axis is time. A vertical line represents stationary and a line at a 45 degree angle represents c. Closer to the vertical than 45 degrees represents a speed slower than c. With that in mind, please consider: "near the star the warping of spacetime by the mass of the star causes the light rays to be at a smaller angle to the vertical."

Going to work, I drive 60Mph west, on the way home I drive 60mph East. Same speed different velocity.

What! No response to my reply to your Einstein quote? going try and simply ignore it, perhaps?? Just trot out another quote from another book that you thought you understood. Nice tactics, how to keep the argument going and convince yourself you are ahead. Ignore your failures and move on to a new and different misunderstanding.

OK. I'll grant you that constant speed does not mean constant velocity. My Einstein quote does not contradict what you said. Happy? Good.

It appears to me your understanding of basic physics is not even at the Halliday and Resnick level. (ie not able to appreciate the difference between velocity and speed, consider a square root to be a "fancy equation" )It would do you well to move beyond the coffee table physics books and attempt to learn the real deal. Start with a calculus text. Move on to a college level Physics text. Open your mind a bit, currently you are blinded by preconceived notions and crippled by your lack of formal physics knowledge.

In college, I studied calculus, advanced calculus, topology, and physics (not advanced physics). I graded the homework for elementary differential equations. I always try to keep an open mind, and I look forward to learning new things. Everyone has their preconceived notions, I suppose.

When I said "fancy equations" that was a failed attempt at humor. I now wish I had not said that. I do not consider square root fancy.

The event horizon separates the universe from the black hole, what is different inside the event horizon? According to your man Hawking, inside the event horizon geodesics form closed paths. Thus light that enters a black hole tangent to a interior geodesic follows that path endlessly.


Hey I thought these were Hawking's ideas. You did read Brief History of time ? Perhaps I got it out of the collection of lectures by Hawking and Penrose.

I don't know enought to say that you are definitely wrong, but that does not sound right to me. My copy of A Brief History of Time is packed away somewhere.

If this is going to turn into a discussion of GR I will move the thread to the appropriate forum where mentors, with better knowledge of the details then I, can answer your questions.

Well, the question of whether the speed of light is constant in a general reference frame does fall under relativity. If you feel the mentors in another forum would be better suited, that is your decision.

 

[Integral]

If you wish to pursue the implications of a variable speed of light, read Faster then the Speed of Light by Joao Maguelijo. The first half of the book discusses the current understanding of GR. I found this to be an excellent presentation. He spends a significant amount of text complaining about the rigidity and short sightedness of the current technical journal system. For him to seriously address, or even discuss, the idea of a variable speed of light was careerer threating. He and a colleague (who was the senior researcher, chickened out at the last minute, refusing to present their initial work or attach his name to it.) developed the theory behind locked doors. The implications of a variable speed of light are far reaching and fascinating. Find a copy and give it a read. But meanwhile this is still very controversial physics and not an appropriate topic for this forum.

But as I said earlier any real discussion of VSP must take place in the Theory Development Forum.

 

[jdavel]

Integral said: "We live deep in the suns "gravity well". this means that, according to GR, Space time is not flat in our vicinity."

At the Earth's surface, the gravitational force of the sun is nearly negligible to that of the earth. In fact it's even small compared to that of the moon, which is why tides are more dependent on the moon than the sun. So wouldn't any curvature of space time near the Earth be caused almost totally by the earth?

 

[Integral]

Clearly the sun has some significant effects. After all we orbit it, this is the gravitational well I am speaking of. As you mention the Earth has significant and noticeable gravitational effects, we walk the surface.

We still measure the speed of light as a constant.

Jdavel,
Are your comments addressing this issue or just to disagree with something I have posted?

 

[jdavel]

Integral,

No, I wasn't just trying to be contrary. Somebody else had suggested a thought experiment involving an accelerating rocket. I thought you had said that space time where we live is curved a lot more than it would be in a rocket because we live "deep in the sun's gravity well". But since the gravitational field at the Earth's surface is almost totally caused by the Earth itself, and since it only causes one g of acceleration, any effects predicted by GR would be greater in a rocket accelerating at more than one g, which is not unreasonable for a rocket. That's all I meant.

 

[Integral]

Ok,
I think even Earth's gravitational well should be sufficient for the argument. After all any acceleration of more then 1 g for any significant amount of time is not a reasonable expectation of a human. (please do not quibble with the phrase "signifiant amount of time". significant >= 1 year. or what ever.

I am becoming more and more convinced that the SPEED of light will be a constant even if the velocity is not.

 

[chroot]

The speed of light is, according to current theory, always constant. The speed of light, as measured by experiment, is always constant. The speed is 1 light-second per second. Feel free to convert to your favorite units ad infininitum.

If you'd like to advance a new theory as a replacement of existing mainstream theory, you are welcome to do so in the Theory Development subforum.

If you'd like to argue that existing experiments don't reflect reality, I suggest that you begin looking for a new universe in which the experimental results better suit you.

Case closed.

- Warren

 

[DrMatrix]

The illustration I referred to in my previous post from The Universe in a Nutshell is a spacetime diagram where the path of light rays' slopes vary from almost vertical near the surface of a star to 45 degrees further away. I was under the impression that the inverse of the (absolute value of the) slope in a spacetime diagram is proportional to speed. Yet this does not indicate a change in speed. I don't understand how that can be.

Case closed.

Fine.

 

[chroot]

I was under the impression that the inverse of the (absolute value of the) slope in a spacetime diagram is proportional to speed. Yet this does not indicate a change in speed. I don't understand how that can be. Fine.

You're forgetting time dilation.

- Warren

 

[DrMatrix]

What time dialation? There is only one reference frame and only one time axis. In order to say there is time dialation, don't you need to say time dilation with respect to something?

 

[Janitor]

Well

John Baez seems to be all over the map on this issue. I will quote a chunk from this page of his:

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html

Since Einstein talks of velocity (a vector quantity) rather than speed it is not clear that he meant the speed will change but the reference to special relativity suggests he did mean so. This interpretation is perfectly valid but a more modern interpretation is that the speed of light is constant in general relativity.
The problem here comes from the fact that speed is a coordinate-dependent quantity, and is therefore somewhat ambiguous. To determine speed (distance/time) you must first choose some standards of distance and time, and different choices can give different answers. This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c.
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.
If general relativity is correct then the constancy of the speed of light, in inertial frames is a tautology from the geometry of space-time. The causal structure of the universe is determined by the geometry of null vectors. Travelling at the speed c means following world-lines tangent to these null vectors. The use of c as a conversion between units of metres and seconds, as in the SI definition of the metre, is fully justified on theoretical grounds as well as practical terms because c is not merely the speed of light, it is a fundamental feature of the geometry of space-time.
Like special relativity, the predictions of general relativity have been confirmed in many different observations. The book by Clifford Will is an excellent reference for further details.
Finally we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies.

How is that for waffling?

 

[Integral]

My guess, is that Einstein was referring to the fact that light in SR is not only assumed to be constant speed but also constant velocity. In SR light always moves along a single coordinate axis, the only direction change occurs at the surface of a mirror. This pure rectilinear motion of a beam of light is strictly constant velocity. While it is not said specifically it is certainly built into his derivations. A nit picker could claim that the curvilinear motion of light in GR is a contradiction of SR. Because SR is developed for constant velocity light only.

 

[Thomas2]

Has anyone an idea why speed of light is constant ? Has this something to do with lack of mass of a photon because I cannnot imagine it to be possible to add speed to something that has no mass. As light emerges from energy fall of an electron, does speed of light have anything to do with rotation speed of an electron ?

The speed of light is constant because, unlike ordinary waves, light propagates without a carrier medium and you don't therefore have an absolute reference frame you could refer the speed to (at least not in a vacuum). The trick of nature is here that a light wave carries itself, or to be more precise, the electric wave carries the magnetic wave and vice versa (as given by Maxwell's equations). The irony is that even Maxwell apparently did not realize this and believed in the Ether Theory and a positive outcome of the Michelson-Morley experiment.
For related aspects see my webpage http://www.physicsmyths.org.uk/lightspeed.htm .

 

[Nereid]

John Baez seems to be all over the map on this issue. I will quote a chunk from this page of his:

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html

How is that for waffling?

Thanks Janitor, this is excellent! Let's take time to go through it slowly, because it deals with nearly all the questions raised on this thread.

 

[Integral]

Frankly I see no sign of waffling in his conclusive statement.

Finally we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies.

 

[DrMatrix]

I see no waffling in this statement:

This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c.

But when you look at that quote next to Integral's quote, the man sounds like he's running for office.

 

[jdavel]

Integral said: "My guess, is that Einstein was referring to the fact that light in SR is not only assumed to be constant speed but also constant velocity."

Another possibility: Either Einstein or the German to English translator was a little sloppy with the German words for velocity and speed.

Anyway it's clear from the English translation of Einstein's own words, that what he was talking about is what we call "speed". From the 1905 paper: '...light is always propagated through empty space with a definite velocity c..." And from chapter 7, paragraph 1 of his book "Relativity The Special and General Theory": 'The assumption that this velocity of propagation is dependent on the "direction in space" is in itself improbable.' Neither of these is consistent with the term "velocity" being a vector.

By the way none of this has anything to do with whether, according to GR, the speed of light in a gravitational field is a constant. Surely the math of GR eliminates any ambiguity, just as the math of SR does.

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.