Einstein's special theory of relativity

Spaceship has mass, a person has mass, and according to mass the velocity of light is constant. This is not very new. BUT: I read two interesting web sites: speed of light isn't constant by them. The first one is about fast light: http://www.rochester.edu/news/show.php?id=2544, the second one is more exiting: www.lajtner.com If I understand it right, the author has a new theory which means that the relativity theory is true, but it is a part of a new theory. Unfortunately both sites are drafts and both are very short.
P.

 

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The length and time, and therefore the speed itself, are as measured in the observer's reference frame. That's what's meant by "relative velocity." Measurements "relative to X" mean "in X's rest frame." It's the only definition of any practical value. Most speeds under most transforms (this definition is not specific to the Lorentz transform) are variant.

The definitions of "speed" and "velocity" are simple, consistent (it doesn't matter what it is you are measuring the speed of), practical (ie. in terms of directly measurable quantities - namely a standard length and time unit in the observers reference frame), and intuitive (reflects the human intuition of speed). What more do you want?

 

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Does anyone here actually even believe that Einstein stole some of his material at the patents office he worked in? geez

 

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The usual definitions of "speed" and "velocity" are not consistent as far as the propagation of light is concerned, because the Galilei transformation (which would imply a frame dependence of the velocity) can not be applied. On the other hand, the standard length and time units, being standard units, can not be changed either (as Einstein attempted to do with this Lorentz transformation). So the only solution here is to use a different concept of 'speed' where the travel time of the light signal does not depend on the velocities of source or observer at all, but only on the distance between them at the time of emission of the signal (see my page regarding the Speed of Light and Theory of Relativity)

Thomas

 

The "usual definitions" of speed and velocity are in no way tied to the Galilean or any other transformation, nor is there any reason for them to be.

The definition of the second is (quote from Wikipedia):

and the metre is:

Both are frame dependent and affected by relative velocity, and transform from one inertial frame to another according to the Lorentz transformations. While the definitions of both units have been revised on numerous occasions (scientists can do whatever they want with their units), it's worth noting that this was never done for the sole purpose of keeping c invariant. The most recent definition of length was only introduced in order to give c an exact integer value, for example.

This would involve selecting one reference frame as the base frame in which all lengths and time intervals are measured (ie the only frame in which the above definitions of speed and time are used). Because only one frame would exist in which measurements could be made, there would be no need for coordinate transformations or any basis in the concept of relative velocity. Basically you'd be forcing c to be invariant across all frames by only allowing one frame. Not only are these arbitrary restrictions an unnecessary hindrance, but this kind of invariance is not the kind that was measured in any experiment.

Whatever you call it, or however you define speed, it was dx/dt for light that was found to be invariant using local x and t coordinates. c was found to be invariant according to the "usual definition" of speed. If you attempt to redefine speed, showing that the "tsmid speed" of light in a vacuum is invariant will in no way explain why the Michaelson-Morley experiment measured an invariant "classical speed" of light.

 

Lorentz transformaitons are not the only possible way to derive time dilation or length contraction. Look up some older threads.

 

Yes, but he stole the ideas and textmaterial from scientific articles,
and most of the material he plagiarized is worthless as science.

Ingvar, Sweden

 

przyk,

This frame is already in widespread use, in astronomy and astrophysics as examples. It is the rest frame of the CMB, of course. The speed of light has to be invariant in this frame, or it has to be invariant wrt the emitter. Experiments indicate that the speed of light is not invariant wrt the emitter, but may be invariant wrt the rest frame of the CMB.
As far as the Michaelson-Morley experiment is concerned, the results have to be viewed as inconclusive. They 'measured' the speed of light as 'invariant' in a medium. We know that is not true, so of what benefit is the experiment in determining if the one-way speed of light is measured as invariant wrt all inertial observers' rest frames in a vacuum? Special Theory is based on this postulation, but it is very suspect. Place a triangular-shaped laser interferometer in a vacuum and pass a signal around the perimeter in opposite directions while the interferometer rotates, such as the LISA experiment, and the experiment can detect its own rotational motion, measure it's own rotational velocity wrt... what, the CMB rest frame? The gravitational field of the sun? I suspect the rest frame of the CMB, but I am not certain. I do know the signal takes longer to make a circuit when emitted in the direction of 'rotation' than an identical signal emitted counter to the direction of rotation. This is, of course, called the Sagnac effect, but the question is what is the interferometer-in-space rotating relative to? The timer-detector that measures the transit times of both signals is located at the point the signals are emitted/detected, rotating with the interferometer.

 

There's a difference between a community using a particular frame consistently in all their measurements as a convention, and a law being invented that explicity outlaws all other frames from being used, or denies their existence.

It's not very difficult for a speed to be invariant if all you have is one frame.

The SR answer is "with respect to all inertial reference frames." Also, you don't need to bring up gyroscopes or the Sagnac effect to show that rotation is in some sense absolute. Imagine a photon (in a vacuum) forced to travel in a large circular path, and imagine yourself at the centre of this circle always turning to face the photon. You'll have just found a rotating reference frame with a stationary photon in it.

 

Perhaps with respect to the local space-time, which I think you can call an ether if you like. Just be careful about what qualities you attribute to it. Velocity? No. Rotation? I'm not sure.

Here's a quote from Einstein:

Generalising we must say this:—There may be supposed to be extended physical objects to which the idea of motion cannot be applied. They may not be thought of as consisting of particles which allow themselves to be separately tracked through time. In Minkowski’s idiom this is expressed as follows:—Not every extended conformation in the four-dimensional world can be regarded as composed of world-threads. The special theory of relativity forbids us to assume the ether to consist of particles observable through time, but the hypothesis of ether in itself is not in conflict with the special theory of relativity. Only we must be on our guard against ascribing a state of motion to the ether.​

And later in the same lecture:

Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.
But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.​

Sidelights on Relativity, 1922. A translation by G. B. Jeffery and W. Perrett of two addresses given by Einstein in 1920 and 1921.

I don't pretend to understand all the implications of this idea, nor how it is interpreted in a modern light. I only found this source a few months ago, and thought it interesting enough to share.

I'd like to have a better intuitive grasp on 4D Minkowsky geometry. It's too hard to visualise these things without falling back into a 3-space + absolute time paradigm.

 

Relative to any inertial frame.

-Dale

 

The present definition of the meter is quite obviously a blatant attempt to make a theory (i.e. Relativity) rather than some standard units the basis of physical measurements. One should note the circular definition we have now: a meter is defined as the length of the path travelled by light (in vacuum) during a time interval of 1/299,792,458 of a second (http://en.wikipedia.org/wiki/Metre ), and the speed of light is defined as 299,792,458 meter/sec (http://en.wikipedia.org/wiki/Speed_of_light ). It suggests that we know both quantities exactly, but we don't, because it all depends how accurately you can measure the time it takes for the light signal to travel a certain distance. So why not stick with the old definition of the meter based on the wavelength of a certain atomic transition?

Only if one re-scales the x and t coordinates by the γ factor so that c is invariant by default.

In the Michelson-Morley experiment, both the source and observer are at rest relatively to each other (i.e. v=0) , so you would not expect any observable effect with either interpretation of "speed".

Thomas

 

No, previous definitions of the metre were also frame dependent. Because of length contraction, you have to specify a frame in your definition of the metre. Let's say the metre was defined as the length of a particular metre stick (more or less how it was done until a good forty years after relativity was published). If the length of this stick is velocity-dependent, you have two choices (choices because there's no way you can show, by logical arguments, that a standard length *should* be defined one way or another - it's simply a matter of convenience):

• Define the metre as "the lenght of the metre stick when at rest with respect to [specify some frame, eg. the CMB]."
• Define the metre locally as "the length of the metre stick when at rest with respect to the observer."

You can adopt the former definition if it helps you sleep at night, but most of the scientific community would never accept it. Fixing the definition to a particular frame would make measurements more difficult, and the results less intuitive. If you decided to use the concepts of relative velocity and coordinate transforms, you'd basically be forced to use the Galilean transformation and its associated velocity addition formula. Because the fundamental laws of physics do not remain invariant with respect to this transformation, measuring instruments, such as rulers, would have to be constantly recalibrated depending on their orientation and velocity relative to the base frame, if this velocity became significant, and the ways laws were applied in calculations would be velocity dependent. Not only is this inconvenient, but it would hide the symmetry already present in the laws of physics - with respect to the Lorentz transform.

This isn't a problem if the metre, by this definition, is affected by relative velocity the same way as it was by previous definions. Also, there's nothing circular in this. The unit of length is defined in terms of the speed of light instead of the speed of light being defined in terms of a standard unit of length. This definition only becomes a problem if the metre becomes direction dependent - ie 1 metre to the left + 1 metre to the right = something other than your original starting point.

How accurately the length of the metre can be known is limited regardless of the definition used.

As I said before, it was done for the convenience of giving c an exact integer value. The end result was basically to adjust the length of the metre a little. Personally, I don't care too much about the details of how the metre is defined.

Yes, and if not only your coordinate system, but all the laws of physics and all your measuring instruments scale the same way, you are justified in doing so. The Lorentz transformation was introduced to explain the observed invariance of the speed of light. You make it sound like someone has gone to great lengths to force the invariance of c by definition, regardless of experimental observations. This is not the case.

The speed of the source is completely irrelevant. All it can affect is the frequency of the light - not its speed. This is a result of Maxwell's theory of electromagnetism. As for the effect the observer's speed has on the relative speed of light, this is dependant on how the observer's measuring instruments are affected by the observer's motion. The Galilean transformation predicts a variant c, according to the Galilean velocity addition formula.

 

I would not consider the integer value of c as more than a coincidence. If the speed of light would have been known with a much better accuracy, I doubt that they would have dropped several significant digits only in order to have an integer value.
Anyway, in practice it all boils down again to how accurately you can measure the derived unit (in this case the meter). Whether or not c has an integer value is completely irrelevant in this respect.

This is only on the basis of the Lorentz transformation. Even if you apply the length contraction in this sense, it is hardly an issue which would complicate matters as there are numerous other effects which have to be taken into account. Just look at the number of complicated corrections which have to be applied to determine distances with the GPS system. Correcting for a length contraction would be rather trivial compared to this.

The present definition of the meter is not just a different definition than before, but effectively it means that the physical notion of a length standard has been abandoned altogether. Of course, in astronomy for instance it is already practice for a while to measure distances in terms of light times (e.g. 'light-years'), but this was merely a practical thing and not enforced by the definition of distances.

With the new definition for the meter, the velocity of an object at distance x for instance becomes now

v=dx/dt = c*dT/dt ,

where T is the travel time of the light signal to the object. Now the point is that T depends on the theoretical interpretation you are giving to the principle of the invariance of c. Special Relativity yields a different value for T than the assumption of a complelety velocity independent travel time I suggested (see my pages Speed of Light and Theory of Relativity and in this context also Speed of Light and Anomalous Acceleration). Such a theory dependence of the standard measuring units is not acceptable (especially if the theory re-interprets the standards as re-scaleable parameters).

Well, if the speed of the source is irrelevant for the travel time of the light signal, so should be the speed of the observer, as it is merely a question of which one you choose as the rest frame (which can not possibly have an effect on the physics).
The point with the Michelson-Morley experiment is that all its components are at rest with regard to each other, so there is no reason why the light travel times in one direction should be affected differently to that in another direction.

Thomas

 

What Einstein should have realized is that the usual idea of motion (i.e. a velocity dependent linear transformation) can not be applied to light. Light is in fact its own ether. It does not need any carrier medium, as according to Maxwell's equations, the electric wave carries the magnetic wave and vice versa (see my page Speed of Light and Theory of Relativity for more).

Thomas

 

Why would it surprise you? This isn't the first time standard units have been defined in such a way as to simplify or eliminate proportionality constants.

Agreed, but this is not a problem for the definition.

This is on the basis of reality and experimentation. While I don't know any experiments that have directly measured relativistic length contraction, one can confidently predict that it occurs. The fundamental laws that govern the structures of physical objects are all Lorentz-invariant. Where they exist, the Galilean-invariant versions of these laws are invariably less accurate than their more modern counterparts.

I never said anything about technical difficulties in defining a standard length. The lengths of physical objects are velocity dependent, so a definition of the metre that doesn't specify a frame is ambiguous and useless. The current convention is to define multiple coordinate systems, each with their own local standard length.

No, there's still a standard unit of length, and it is still the metre. Its definition doesn't prevent it from being used as a standard unit.

Why should the way standard units are defined be constrained by your personal feelings about what is and isn't acceptable? Requiring the length and duration of the metre and second respectively to be frame invariant quantities seems like an arbitrary (and unhelpful) restriction to me.

No, that doesn't follow. If the speed of light is unaffected by the speed of the source, it implies either a preferred frame or invariance of the speed c.

The fact that the choice of rest frame has no effect on the physics is not self-evident, and it is dangerous to take it for granted as you seem to be doing. In most cases the coordinate system used does affect the laws of physics. A simple example is accelerating frames (at least as far as classical physics and STR are concerned - I won't pretend I know how GR handles them). In Newtonian physics, F=m(dx/dt) becomes F=m(dx/dt-a), where a is the frame's acceleration with respect to an inertial frame. Effects like this also appear in rotating frames.

The question is whether frame-dependent changes to the laws of physics, like the example I just gave, appear during constant-velocity coordinate transforms. With classical physics, it could easily be demonstrated that the laws remained invariant with respect to the Galilean transformation, which made the laws velocity-independent. This was fine until electromagnetism was found to be velocity-dependent with respect to the Galilean transformation. It was found to be velocity-independent if one used the Voigt or Lorentz transform, but not the Galilean. Because the two branches of physics were not invariant with respect to the same set of coordinate transformations, it implied a preferred frame - the only frame in which both mechanics and electromagnetism would hold in their standard forms.

The first postulate of relativity requires all the laws of physics to remain invariant with respect to a common transformation. In light of this, classical mechanics was modified to make it Lorentz-invariant (basically with the introduction of relativistic momentum, ie. p=mv replaced by p=γmv). The fact that experiments, where they can distinguish between the two, support relativistic mechanics over classical mechanics constitutes, in my opinion, far stronger evidence in favour of relativity than the Michaelson-Morley experiment ever was.

Yes there is if length and time are frame-invariant. If light travels at c only in some preferred frame, it will travel at c-v with respect to the source, if v is the source's 'absolute' velocity. Invariant length and times directly contradict the invariance of c and its independence on the velocity of the source. The only possible way around this is to play on the definition of relative velocity which, in addition to being wholly unjustified, does not explain the observed invariance of c measured according to the usual definition of speed.

 

Hello all
The speed of light is independant/unaffected by the speed of the emission source. This was proven in an experiment at CERN in 1964 involving relativistic neutral pion particles. However, the velocity of a emission source does affect the direction of the emitted light. Look at the above experiment (if you can find it: my link is know a 404 error) or at synchrotron radiation. What puzzles me is that I cant find any experiment/info on the gamma ray photon emission angle for a neutral pion at rest. This should be 180 degrees but this hasn't been measured. One does wonder.

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Someone should tell that to MacM and his Extinction Shift guy...

 

As many times as this has been claimed, I have never seen any explanation of how Special Relativity does this. Are we just supposed to " take it from you "? A little less conversation, a little more EXPLANATION, please.

 

If you can't figure it out yourself (it's intuitively trivial, you know), then try here.