Two speed of light experiments at different altitudes

[kmarinas86]

so what data does he have to support the idea that light does not move at the same speed in all strata of the Universe?

Different link: http://www.gutenberg.org/etext/5001

Bibliographic Record Creator Einstein, Albert, 1879-1955
Title Relativity : the Special and General Theory
Language English
LoC Class QC: Science: Physics
Subject Relativity (Physics)
EText-No. 5001
Release Date 2004-02-01
Copyright Status Not copyrighted in the United States. If you live elsewhere check the laws of your country before downloading this ebook.

"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. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlinlited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)."

If you assume a standard clock, say the second on Earth at sea level, you will notice a difference between the second of this clock and the second of a clock on top of Mt. Everest - assuming that these devices are identical. An experiment measuring the speed of light on top of Mt. Everest will give the same result as an experiment measuring the speed of light at sea level. But, now it is obvious that the experiments themselves are being executed at different rates. They're different rates because of how initally synchronized clocks will desynchronize after being subjected to a change altitude - Gravitational Time Dilation.

 

[ZapperZ]

Please don't site someone's website and use it as "evidence". If you wish to challenge established physics, doing it like this will only earn you either a scoff, or dismissal. Find an experimental evidence that has been published in peer-reviewed journals. I can cite several websites that claim to have evidence of ghosts.

I'm hoping that everyone here would at least have some standard in considering the SOURCE of the information. If one learns nothing else from PF, this would be the most valuable piece of awareness that we can provide.

Zz.

 

[kmarinas86]

Please don't site someone's website and use it as "evidence". If you wish to challenge established physics, doing it like this will only earn you either a scoff, or dismissal. Find an experimental evidence that has been published in peer-reviewed journals. I can cite several websites that claim to have evidence of ghosts.

I'm hoping that everyone here would at least have some standard in considering the SOURCE of the information. If one learns nothing else from PF, this would be the most valuable piece of awareness that we can provide.

Zz.

Ok. Maybe using Google wasn't a good idea. But I think this is a legitimate quote from Einstien - I've looked up the quote months ago, and it appears to be authentic - I have the looked at Einstiens paper on GR (but I haven't seen the detailed formulas he wrote). Note that I didn't say Einstein was right. Most scientists agree that Einstein was wrong about black holes and quantum mechanics.

Here is something more appropriate:
http://www.gutenberg.org/etext/5001

Bibliographic Record Creator Einstein, Albert, 1879-1955
Title Relativity : the Special and General Theory
Language English
LoC Class QC: Science: Physics
Subject Relativity (Physics)
EText-No. 5001
Release Date 2004-02-01
Copyright Status Not copyrighted in the United States. If you live elsewhere check the laws of your country before downloading this ebook.

 

[kmarinas86]

http://www.gutenberg.org/etext/5001

Here is the context of that quote made in this thread (not copyrighted):

Albert Einstein: Relativity
Part II: The General Theory of Relativity
A Few Inferences from the General Principle of Relativity



The considerations of Section 20 show that the general principle of relativity puts us in a position to derive properties of the gravitational field in a purely theoretical manner. Let us suppose, for instance, that we know the space-time " course " for any natural process whatsoever, as regards the manner in which it takes place in the Galileian domain relative to a Galileian body of reference K. By means of purely theoretical operations (i.e. simply by calculation) we are then able to find how this known natural process appears, as seen from a reference-body K1 which is accelerated relatively to K. But since a gravitational field exists with respect to this new body of reference K1, our consideration also teaches us how the gravitational field influences the process studied.

For example, we learn that a body which is in a state of uniform rectilinear motion with respect to K (in accordance with the law of Galilei) is executing an accelerated and in general curvilinear motion with respect to the accelerated reference-body K1 (chest). This acceleration or curvature corresponds to the influence on the moving body of the gravitational field prevailing relatively to K. It is known that a gravitational field influences the movement of bodies in this way, so that our consideration supplies us with nothing essentially new.

However, we obtain a new result of fundamental importance when we carry out the analogous consideration for a ray of light. With respect to the Galileian reference-body K, such a ray of light is transmitted rectilinearly with the velocity c. It can easily be shown that the path of the same ray of light is no longer a straight line when we consider it with reference to the accelerated chest (reference-body K1). From this we conclude, that, in general, rays of light are propagated curvilinearly in gravitational fields. In two respects this result is of great importance.

In the first place, it can be compared with the reality. Although a detailed examination of the question shows that the curvature of light rays required by the general theory of relativity is only exceedingly small for the gravitational fields at our disposal in practice, its estimated magnitude for light rays passing the sun at grazing incidence is nevertheless 1.7 seconds of arc. This ought to manifest itself in the following way. As seen from the earth, certain fixed stars appear to be in the neighbourhood of the sun, and are thus capable of observation during a total eclipse of the sun. At such times, these stars ought to appear to be displaced outwards from the sun by an amount indicated above, as compared with their apparent position in the sky when the sun is situated at another part of the heavens. The examination of the correctness or otherwise of this deduction is a problem of the greatest importance, the early solution of which is to be expected of astronomers.1)

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. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlinlited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).

Since it has often been contended by opponents of the theory of relativity that the special theory of relativity is overthrown by the general theory of relativity, it is perhaps advisable to make the facts of the case clearer by means of an appropriate comparison. Before the development of electrodynamics the laws of electrostatics were looked upon as the laws of electricity. At the present time we know that electric fields can be derived correctly from electrostatic considerations only for the case, which is never strictly realized, in which the electrical masses are quite at rest relatively to each other, and to the co-ordinate system. Should we be justified in saying that for this reason electrostatics is overthrown by the field-equations of Maxwell in electrodynamics ? Not in the least. Electrostatics is contained in electrodynamics as a limiting case ; the laws of the latter lead directly to those of the former for the case in which the fields are invariable with regard to time. No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.

In the example of the transmission of light just dealt with, we have seen that the general theory of relativity enables us to derive theoretically the influence of a gravitational field on the course of natural processes, the laws of which are already known when a gravitational field is absent. But the most attractive problem, to the solution of which the general theory of relativity supplies the key, concerns the investigation of the laws satisfied by the gravitational field itself. Let us consider this for a moment.

We are acquainted with space-time domains which behave (approximately) in a " Galileian " fashion under suitable choice of reference-body, i.e. domains in which gravitational fields are absent. If we now refer such a domain to a reference-body K1 possessing any kind of motion, then relative to K1 there exists a gravitational field which is variable with respect to space and time.2) The character of this field will of course depend on the motion chosen for K1. According to the general theory of relativity, the general law of the gravitational field must be satisfied for all gravitational fields obtainable in this way. Even though by no means all gravitationial fields can be produced in this way, yet we may entertain the hope that the general law of gravitation will be derivable from such gravitational fields of a special kind. This hope has been realized in the most beautiful manner. But between the clear vision of this goal and its actual realisation it was necessary to surmount a serious difficulty, and as this lies deep at the root of things, I dare not withhold it from the reader. We require to extend our ideas of the space-time continuum still farther.

 

[Ich]

If you expect an answer, ask something.

 

[yogi]

I am curous about this part of the quote:

"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. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlinlited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)."

In particular, is Einstein saying unambiguously that the G field changes the speed of light - or simply its direction (velocity vector) .. do we know whether an individual photon can be deflected w/o altering its speed?

 

[pervect]

The short version is that,the term "speed of light" is ambiguous. If you use a single clock and ruler at the origin of a coordinate system, the speed of light, thought of as the rate of change of the distance coordinate with respect to the time coordinate, in general changes.

But if instead of using one clock and ruler (at the origin of the coordinate system) one uses multiple clocks and rulers, each located where the light actually is, the speed of light is constant.

Basically one constructs "local inertial frames" around these multiple clocks and rulers, and shows that the speed of light is constant in each of these local frames.

The modern interpretation is to say that the speed of light is actually constant.

Earlier interpretations attached more physical significance to the coordinate speed than modern interpretations do. Einstein's quote is an example of one of these earlier interpretations. Some people like to "stop the clock" at Einstein, I'm not one of them, physics has progressed and changed a little since his time. I like to think it's for the better, even if one disagrees anyone who wants to read a modern textbook will be need to be aware of the modern interpretation.

See for instance

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

which discusses this very quote of Einstein's

Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory. In the 1920 book "Relativity: the special and general theory" he wrote: . . . 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 [. . .] 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. Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. This interpretation is perfectly valid and makes good physical sense, 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 moved/time taken) 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 generalisation 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.

 

[Integral]

There can be no misunderstanding of the quote if you understand that when Einstein says VELOCITY he means velocity. Velocity is a vector quantity so is composed of 2 components, speed (magnitude) and direction. The magnitude of the velocity of light is ALWAYS c. However the direction of the light is changed by massive objects, so the VELOCITY of light is not always constant.

 

[jtbell]

Some people like to "stop the clock" at Einstein, I'm not one of them, physics has progressed and changed a little since his time.

To put it another way, physics is not like literature. When you study Shakespeare's plays, you always study Shakespeare's own words. Anything else just isn't Shakespeare!

Physical theories are different. Einstein deserves great respect as the primary original creator of relativity theory, but the theory, after its creation, does not depend on Einstein's own words. Physicists have been working with relativity for over a hundred years, over half of them since Einstein died. At this point, Einstein's writings on relativity are mainly of historical interest. This doesn't mean they're worthless, of course, but we have to put them in the context of our current knowledge.

 

[yogi]

pervect - thanks for the tutorial. I see from the article I was not the only one to be puzzled by what Einstein was trying to say, or whether he was even correct in what he was attempting to state.

 

[pervect]

There can be no misunderstanding of the quote if you understand that when Einstein says VELOCITY he means velocity. Velocity is a vector quantity so is composed of 2 components, speed (magnitude) and direction. The magnitude of the velocity of light is ALWAYS c. However the direction of the light is changed by massive objects, so the VELOCITY of light is not always constant.

There is a more fundamental ambiguity issue here, though, which goes beyond what Einstein's intentions were when he wrote this quote. Baez, in his GR tutorial, talks about this issue a little bit:

http://math.ucr.edu/home/baez/einstein/node2.html

Preliminaries

Before stating Einstein's equation, we need a little preparation. We assume the reader is somewhat familiar with special relativity -- otherwise general relativity will be too hard. But there are some big differences between special and general relativity, which can cause immense confusion if neglected.

In special relativity, we cannot talk about absolute velocities, but only relative velocities. For example, we cannot sensibly ask if a particle is at rest, only whether it is at rest relative to another. The reason is that in this theory, velocities are described as vectors in 4-dimensional spacetime. Switching to a different inertial coordinate system can change which way these vectors point relative to our coordinate axes, but not whether two of them point the same way.

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.

This is exactly the heart of the problem with the ambiguity of the velocity of light. There is no problem as long as one is restricted to measuring the velocity of light in a "small" inertial frame. One can safely say that the velocity of light, locally, is always equal to 'c' - because one can compare velocities if they are at the same point. When the frame is small enough, the curvature effects become irrelevant.

The very concept of comparing a velocity at one point in space-time to the velocity at another distant point is not in general unambiguously defined.

In practice, people (cosmologists, for instance) often adopt some specific coordinate system, and use the rate of change of a distance coordinate with respect to a time coordinate to find the 'velocity' of a distant object. This procedure can and does result in the 'velocity' of light at a distant location as not being equal to 'c'. The procedure depends entirely on the adoption of some specific coordinate system, so it is not very "physical" as the results are coordinate dependent.

However, any procedure that locally measures the speed of light (by setting up a small, local coordinate system at the same point in space-time where the light beam itself is located) will always get 'c', without running into this issue.

The short version is that the speed (coordinate speed) of light is always locally 'c', but not necessarily globally equal to 'c'.

The modern interpretation is to focus on what is invariant (the local velocity of light as measured by the observer in a small-enough frame with his clocks and rulers), and not worry about what changes (the velocity of light at a distant location in some specific coordinate system).