Relativity is broken"Relativity Broken: Uncovering the Mystery

[quantumdude]

The speed of light c is a “unit” that was defined by Einstein in order to provide a common measure in the newly invented time-space geometry. It is a useful “unit” for the “accountants” that we call Physicists of applied Physics, and also for the theoretical Physicists.

Physicists are not accountants.

The speed of light was not measured or calculated and then found to be always constant.

The speed of light has been both calculable from Maxwell's electrodynamics and accurately measureable since the late 19th century, which is before 1905 when Einstein postulated its frame-invariance.

The speed of light is taken to be constant in the context that, Einstein accepted two axioms. First that, light is accepted to have a common and identical way of physical being in all references, according to the measurements regarding them, therefore the speed of light is constant. Second, all other physical entities and phenomena have the same universal analogy when they are compared to themselves while being in a state not accelerating (this means that the laws of physics are universal as they are being measured).

The phrase "way of physical being" is ill-defined at best. The postulates are simple and straightforward, and they do not read that way:

Examples of this sort, together with the unsuccessful attempts to discover any motion of the Earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.1 We will raise this conjecture (the purport of which will hereafter be called the ``Principle of Relativity'') to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies.

Therefore the speed of light becomes in itself the measure that measures the values of the time-space dimensions.

Only people can measure things. The speed of light doesn't measure anything. It is just a conversion factor between space units and time units. The units of space and of time are only different because that particular convention was adopted before Einstein placed space and time on equal footing.

In natural units, c=1.

Thus, the constancy of the speed of light is conventional. I am sure you know all that.

In 1964 the one-way speed of light was measured from fast moving \pi^0 mesons, and it was found to be c. You can't force that outcome by convention.

Reference: Alvaeger F.J.M. Farley, J. Kjellman and I Wallin, Physics Letters 12, 260 (1964).

To ask whether space/time change, or clocks/rulers change is not a quantitative question. It is fine to ask this question, but this goes beyond conventional evaluation seeking the actual values of physical dimensions.

I can't make heads or tails of this bit. What is a physical dimension, and how does one assign a value to it?

Until our days, Science of Physics has never found the actual values of any physical entity and has always used conventional “units” in order to evaluate physical orders in reference to these units.

This is not true. There are many dimensionless quantities in physics. You just have to do a little homework to look them up.

The science of Physics can not exist without “units” (or at least has not done that yet) –

Why can't it? What is it about, say x^{\prime} = \gamma (x-vt) that committs me to a particular system of units?

without a measure the physics entities become dimensionless and cease to have a scientific physical substance.

Actually, the more prevalent view is that dimensionless quantities are the only quantities that are scientifically meaningful.

 

[leandros_p]

In natural units, c=1.

Dear Tom Mattson,

You use using definitions and "units" and results of measurement and of calculations, and at the same time you refuse to acknowledge the difference between a measured value and an absolute value.

Einstein, by saying that the physical value of c=1, created a whole new mathematical/physical system and a whole new physical geometry, just like mathematicians defined the square root of minus one (i), which produced the mathematics of complex numbers.

To support that the speed of light was measured/calculated to the value of 1, or c, it’s like saying that the value of the complex number i is measured/calculated, or it’s like a classical physicists saying that he can measure a kilogram of mass without a system of “units”. The classical physicists can not evaluate a mass without a system of units because without a system of units he does not has a “counterbalance” to make the comparison of the measured mass, neither in the lab, nor in theory. Both, the lab and the theory need specific well defined system of units.

There is no way to express an absolute physical value without specifying a comparative relation of this absolute value to another one. That other value becomes the measure/unit of measurement, either directly or indirectly. Even the number 1 is not an absolute mathematical value. It is defined with specific mathematical definitions, and only then it becomes a mathematical “unit”. You measure/calculate “one” physical entity but the physical value of this is not one, unless you define the value of “one” in your system according to a specific mathematical/physical unit.

In 1964 the one-way speed of light was measured from fast moving \pi^0 mesons, and it was found to be c. You can't force that outcome by convention.

Reference: Alvaeger F.J.M. Farley, J. Kjellman and I Wallin, Physics Letters 12, 260 (1964).[\QUOTE]

This is exactly your main misunderstanding. (unless you refer to a measurement of a local system of reference, which has nothing to do with the universal “speed” of light that is defined by relativity). I do not say that the measurement was forced by convention. I just say that the value of the speed of light was not measured at all. In order to perform a physical measurement we need a scale. If the unit of the scale is the speed of light, we do not need to measure the unit of the scale, in the context that we know its value without any physical measurements and calculations – it is known just by definition.

While science of Physics calculates one physical value in relations to another physical value, you support the idea that a measurement makes the measured values to be recognised as absolute values. If I measure a speed compared with another speed and I found them to be equal, I had made a perfectly valid measurement, but I have no idea about the actual value of these speeds as a value. Therefore each time I want to evaluate the physical value of any speed, I have to compare it to a specific constant and well defined “unit” of speed, or to compare it to another already measured speed in order to calculate a speed in reference to the defined unit analogically. The same methodology is used in theory and in the lab.

This constant relative comparison to a defined “unit” is not required for the speed of light, because Einstein defined the speed of light to be acknowledged as the “unit” of simultaneous measurement of “time” and “space”. Therefore, we do not measure the speed of light; we accept that light has a constant speed in every reference system, and that all physical laws are universally identical, and because of those two definitions we can define the unit “speed of light”=1.

The result of these two axioms makes any value of time and any value of space to be expressed only in calculated/measured relative values in reference to the speed of light And as a mandatory aftermath, in physics of relativity, every time that we measure/calculate the value of time we also make a measurement/calculation of the value of space and every time that we measure/calculate the value of space we make a measurement/calculation of the value of time, in reference to the speed of light.

Actually every speed, including the speed of light, has no absolute mathematical value when it is expressed by the physics of relativity, according to the mathematical system that emerges from the two axioms of relativity. On the contrary, relative values –and only relative speeds - can be measured/calculated for any speed in every system of reference, when we use as reference the conventional value of 1 (or value of c, depending of how we define the speed of light).

Therefore, when time/space are measured/calculated with different values, from different systems of reference, we accept the measurements/calculations as long as our initial hypotheses are both valid in our lab, and in our calculations, that is, the definition of the speed of light equal to the value 1 (or c, depending of how we want to scale our unit) and the commonness of universal laws of physics must produce analogical results.

The question: “which is true, time/space change, or clocks/rulers change?”, as it was expressed, is not referring to the values of the measurement/values of time/space or of clocks/rulers, but it seeks to find the cause(s) that are producing the changes of values in an absolute way. It seeks to define the absolute values of time/space by expressing the intrinsic physical way of being of time and of space.

But Physics had never expressed such absolute values. The science of Physic just calculates/measures relative physical relations among classes of physical objects and phenomena, using mathematics and logic (which can be expressed in mathematics as well).

Leandros

 

[JesseM]

In 1964 the one-way speed of light was measured from fast moving \pi^0 mesons, and it was found to be c. You can't force that outcome by convention.
Reference: Alvaeger F.J.M. Farley, J. Kjellman and I Wallin, Physics Letters 12, 260 (1964).

How was this done, exactly? If multiple clocks at different locations were used, then the speed would depend on what convention you use for synchronizing different clocks. It is possible to construct coordinate systems where the two-way speed of light is still c but the one-way speed is not, by using a different clock synchronization convention then the standard one. So it seems to me that all statements about one-way speed depend on your choice of clock synchronization convention, although the standard convention is certainly the most "natural" one because it's the only one each observer can physically realize without reference to any external landmarks, and also because it insures that the laws of physics will work the same way in different frames.

 

[Albrecht]

But you PICK AND CHOOSE which physicists to "accept". What about the large number of those who disagree with your view? What happened to those to interpret the Sagnac effect differently than yours? Why do you ignore those?

At least there are different interpretations of the current SR, so that different authors come to different conclusions. And there is, as I wrote before, an even more controversy discussion regarding the Ehrenfest paradox.

I see that you have a great problem to accept that the current physical theories are in fact not complete but to some extent approximations. (These approximations can in fact be extremely precise, see Newton and Maxwell). But why do you worry? If our theories would be complete and final, the physicists in research could retire. Perhaps we will have this after the Grand Unified Theory (GUT) has been found.

You were very deceitful in using this effect as "proof" that relativity failed WITHOUT mentioning that there are many published papers that already consider this as consistent with SR. In fact, such effects are already being used for ELECTRONS producing phase shift very much similar to the Ahranov-Bohm effect. Would you like a reference for this or are you aware of such things already but didn't want us to know about it as part of your coverup?

I guess that you mean the Aharonov-Bohm effect. - As far as I understand it, it treats the phase shift of electrons in a varying electric or magnetic field. It is stated that there is no phase shift if no field is applied. - The Sagnac experiment is not about any kind of a field. So this seems to be a very different physical situation.

If we re-think SR then:

In a first stage of a discussion about SR the question is not, whether SR is correct or failed. But fact is, that there is another base to develop SR from, which results in the same Lorentz transformation.

In a second stage we can see, that this alternative SR is easier to understand and avoids the permanent conflicting discussions about interpretations (ref. to Selleri).

(And finally we may see that this alternative SR leads to an alternative GR, which is easier to understand and in addition no longer in conflict with QM.)

Such things are VERY unethical. It is irresponsible to use such evidence without pointing out that such interpretation isn't even widely accepted.

As mentioned before, here is a different understanding about whether contraction is a result of a measurement or a physical reality. Most physicists I know believe, that the former is true. For the opinion of Einstein the latter is true. And the latter is necessary to deduce GR from SR.

Because I have good reasons for it, and you were unable to back it up. I asked for where SR has been falsified, you showed the Sagnac effect. Well, we know how well that one flew, didn't we? So now what else?

Did you investigate any paper of Selleri? (One reference is http://www.ba.infn.it/~selleri/R36%20-%20Sagnac.pdf )

At least one can state that there are different interpretations of physicists who’s names guarantee, that they do thorough and reliable work.

You haven't been able to come up with anything else! You pointed out QM as "evidence" that SR is wrong? Now this is crap AND bogus because I asked you why you are ignoring Dirac's work! I'm sure you have heard of relativistic Schrodinger Equation. So why are you claiming such nonsense?

I found this “nonsense” in an issue of the German version of “Scientific American”. -According to the journal, the author was one of the leading US-scientists.

I have already mentioned that the option, to explain dilation by the internal oscillation of elementary particles, can be deduced from the Dirac equation and Schroedinger’s analysis of it. So, why do you state that I ignore both?

Show me something in physics that "was ever proven". I have asked this before.

Again, this is very deceitful. When you asked something like this, it implies that there are already precedent that such a thing has already occured. I put it to you that there's NOTHING in physics that has ever been PROVEN. Experiments can only provide the VALIDITY of any parts of physics.

You are right that I should use a different wording. So now this way:

We learn in our physical lessons that

- Any variation of the speed of light in different frames was disproved
- The existence of absolute motion (or ether) was disproved
- Any possibility to explain SR effects without using Einstein’s concept of space-time was disproved
- The possibility to explain particle-wave by a piloting wave was disproved.

NONE of these statements is correct! But nearly everyone believes them.

...You seem to have ignored a whole set of experimental evidence that continue to test the postulates of SR and continue to get more accurate verifications (not proofs) of their ...

I appreciate such a list, but I am sure that I know most of them.

There is in fact no conflict to any accurate experiment visible to me. If you use the assumption that the physical value of ‘c’ (not the measurement) varies, and if you use the assumptions that fields contract, not the space, and that the internal oscillations of elementary particles are dilated, not the time, then for
ALL of the SR experiments I ever heard of you would get exactly the same results.

Or tell me one experiment which is in conflict with this statement.

...Again, no mention of Dirac or relativistic QM, or even QED!

I referred to Dirac in a previous post. - I do not see at which point QM and QED are in conflict with the alternative understanding of SR as sketched above.

You either are commiting a bad habit for a physicist, which is picking and choosing only what supports you, or worst still, being ignorant and no doing your homework to check if things that you are proposing have already been addressed in one form or another.

Either way, these ruin your credibility as a scientist.

Fortunately only for you, not for others. I have presented those considerations at more than a dozen physical conferences. There was always an interesting discussion. But no one ever used words like “crab” or “bogus”.

I have the impression that there is a lot of misunderstanding between us. I wonder what we can do to make that better.

 

[ZapperZ]

At least there are different interpretations of the current SR, so that different authors come to different conclusions. And there is, as I wrote before, an even more controversy discussion regarding the Ehrenfest paradox.
I see that you have a great problem to accept that the current physical theories are in fact not complete but to some extent approximations. (These approximations can in fact be extremely precise, see Newton and Maxwell). But why do you worry? If our theories would be complete and final, the physicists in research could retire. Perhaps we will have this after the Grand Unified Theory (GUT) has been found.

Again, you have a propensity to deduce from my questioning of your position that I "have great problem to accept...". Where did I mention that? A practicing physicist, BY DEFINITION, works in areas where there is an incomplete knowledge, on things that we currently don't fully understand, or something that is new! Do you think I work in an area simply to REPEAT what is already known and verify? GET REAL! Try getting a research funding to verify Newton's Laws, why don't you?

What I questioned was your "proofs" and how you CONCEAL alternative explanation. And it is IRONIC that you are trying to argue that there are alternative formulation for all the experiments that agree with SR's postulates. Yet, you were using these experiments as IF they are inconsistent with SR. You didn't hesitate to claim that experiments that agree with SR also can be explained by other means, but you wouldn't admit the same thing with the stuff you pointed out.

THIS is what I meant by unethical and deceitful. I put very little credibility in things you are claiming.

Zz.

 

[quantumdude]

Einstein, by saying that the physical value of c=1, created a whole new mathematical/physical system and a whole new physical geometry, just like mathematicians defined the square root of minus one (i), which produced the mathematics of complex numbers.

Einstein did not set c=1. At his time you still calculated c from Maxwell's theory: c=\frac{1}{\sqrt{\mu_0\epsilon_0}}. The c=1 definition did not take hold until much later, as I will make clear below.

In 1964 the one-way speed of light was measured from fast moving \pi^0 mesons, and it was found to be c. You can't force that outcome by convention.
Reference: Alvaeger F.J.M. Farley, J. Kjellman and I Wallin, Physics Letters 12, 260 (1964).

This is exactly your main misunderstanding. (unless you refer to a measurement of a local system of reference, which has nothing to do with the universal “speed” of light that is defined by relativity). I do not say that the measurement was forced by convention. I just say that the value of the speed of light was not measured at all.

Do you seriously think that any group of scientists would measure the speed of light when it is known by definition, and do you seriously think that Physics Letters would publish the results?

I think that you are confusing two different eras in history. That paper was published in 1964, which means that the exprerminent was most likely done when the following NIST standard for a meter was in use:

1,650,763.73 vacuum wavelengths of light resulting from unperturbed atomic energy level transition 2p₁₀ * 5d₅ of the krypton isotope having an atomic weight of 86. The wavelength is λ = 1 m / 1,650,763.73 = 0.605,780,211 µm.

So yes, they did measure the speed of light. It was the wavelength of light from those particular kryptonic transitions that you wouldn't bother measuring.

The definition of the meter in terms of the speed of light didn't come around until 1983. Only in experiments done since that time can we say that the speed of light is not really measured, as long as experimenters hold to current NIST standards. Of course, an experimenter is always free to hold to another standard, and thereby measure the speed of light.

See the following link: Time Line for the Definition of the Meter.

[edit to add]
I forgot to mention an important point. Even if you define the speed of light as a unit of measurement, it still does not follow that measurements of the speed of light from moving sources is meaningless. So if Alvager et al had adopted the 1983 NIST condition it still wouldn't have changed the non-triviality of the experiment. If they held that c=1 it still wouldn't guarantee the Lorentz invariance of light. If Galilean relativity were true they would have obtained a speed of nealy 2c for the photons. It is not true that the constancy (that is, the Lorentz invariance) of the speed of light is just a convention of units and dimensions.
[/edit]


As for the rest of your post, I think we are on two different pages. Naturally, I acknowledge that in order to measure a quantity you have to compare it with something quantity. That's the definition of measurement! What I thought you were saying is that physics only uses quantities with dimension, which is not true. Any equation of physics can be written in a dimensionless form.

How was this done, exactly?

I'll dig up the paper and start another thread.

 

[Albrecht]

... The speed of light is taken to be constant in the context that, Einstein accepted two axioms. First that, light is accepted to have a common and identical way of physical being in all references, according to the measurements regarding them, therefore the speed of light is constant. ... Therefore the speed of light becomes in itself the measure that measures the values of the time-space dimensions. Thus, the constancy of the speed of light is conventional. I am sure you know all that.

For my feeling, your considerations are a bit too philosophical and too complicated. It can be understood and explained in a simpler way.

Michelson has shown that, if the speed of light (i.e. the 2-way-speed) is measured in different moving frames, the same result is received. This was at that time an unexpected result and it has caused a kind of a shock to the physical world.
On the other hand Lorentz has shown that the Maxwell equations can be transformed into any other reference system without making them change.

Now two solution have been offered:

Lorentz has used his calculations about the Maxwell theory to show, that fields in motion have to contract and so also the Michelson apparatus. That explains the result.

Einstein has done a big step and has created an axiom, that the speed of light is constant in all frames.

For my opinion, the understanding of Lorentz is a traditional physical understanding. Einstein’s understanding can be called a structural understanding.

The success of Einstein’s way has a lot to do with the education system in Germany at that time. It was very much related to ancient Greek philosophy. Particularly Plato did have the concept that our world is built by structures. The objects we see around us are - according to him - more a kind of a mental delusion. Based on these considerations Einstein was very soon strongly supported by Max Planck, who liked this kind of a concept. (By the way, the understanding of Heisenberg regarding QM had a similar reason.)

Back to the measurement of ‘c’: Constancy or non-constancy can be measured without any reference to a measurement unit (see the Michelson experiment). And for another solution: In the Shapiro experiment a radar pulse is send to Venus and reflected back to Earth. This needs some time. Now in the moment when the sun moves close to this beam of pulses, the time is extended. The easy way to understand this is that ‘c’ is reduced in the vicinity of the sun (again without using units). - But this explanation is not acceptable by Einstein because his axiom is, that ‘c’ is always constant. So Einstein has to explain that the delay is caused by a change of the ‘space’. According to him (and his followers) we have to assume that the space close to the sun is in some way contracted, so that the photons in the pulse train have to pass a larger piece of space in order to pass the same distance as seen from outside. - And this now is the base of General Relativity as understood by Einstein.

 

[Hurkyl]

Albrecht: in GR, the hypotheses of SR (including constancy of the speed of light in inertial frames) are only required to hold in sufficiently small regions of space-time.

Furthermore, the path traveled by a photon has zero (proper) length. This is true both in SR and GR.

 

[leandros_p]

Einstein did not set c=1. At his time you still calculated c from Maxwell's theory: c=\frac{1}{\sqrt{\mu_0\epsilon_0}}. The c=1 definition did not take hold until much later, as I will make clear below.

For my feeling, your considerations are a bit too philosophical and too complicated. ...

Lorentz has used his calculations about the Maxwell theory to show, that fields in motion have to contract and so also the Michelson apparatus. That explains the result.

Let me say, that you both have a similar way of viewing the physical term "speed of light". Einstein brought a new way in defining - not just using - this physical term “speed of light”. This is not a philosophical difference, but it is a scientific difference.

Generally in Science -and in Physics too- there are two kinds of terms: the “variables” and the “constants”. They are both expressed in values. The difference is that a “variable” has a relative value (which is measured/calculated in relation/ratio to constants), where a “constant” has an absolute value (which is defined in a conventional way).

Einstein introduced a new constant in Physic, that is, he defined axiomatically that the "speed of light" belongs to the class of "constant terms of Physic". That means that its value may be expressed by any system of units (with the value of c, 1, or any other), because the value of the speed of light has an absolute meaning, but then all other values of variable physical terms of space-time should be expressed in relation to the defined constant absolute value of the speed of light.

In this context, when I measure the speed of light, according to Einstein's axiomatic system and I get a specific value, I am not measuring/calculating "the speed of light" but I am normalizing the values of the other variable physical terms that are being involved in the measurement according to "the speed of light".

Therefore, the physical term “space”, as a physical term that is being involved in the measurement of the speed of light as length, lost its absolute meaning as a physical constant and it is nowadays expressed by the speed of light as a variable physical term by the definition of the unit meter . Same thing happened to the physical term "time" by the definition of the unit second.

When we "measure" the speed of light and we get a specific result of 299,792,458 m/s, according to Einstein's axioms, we are actually measuring coinstantaneously BOTH the variable physical terms of “space”, (in meters) AND of “time” (in seconds), by using the constancy of the ratio space/time that is expressed by the physical term “speed of light”.

The number 299,792,458 meters is the measured “space” that light travels in one second and the number 1/299,792,458 is the “time” in seconds that is needed for light to travel the length of a meter. In this context, the value 299,792,458 m/s is the speed of light only in the way that it normalizes the values of "time" and "space"; "space" becomes a variable physical term that can not be defined independently from another physical term, which is "time". And "time" becomes a variable physical term that can not be defined independently from another physical term, which is "space". This cyclical definition of "space" by "time" and of "time" by "space" is normalised by the constancy of the physical ratio “space/time” which Einstein defined as the constant physical term "speed of light".

In an analogy, this is like the relation of the circumference and of the diameter of circle. For any circle, the circumference is expressed by the diameter and at the same time the diameter is expressed by the circumference, and for all circles the ratio of the circumference to the diameter is \pi. The term \pi is expressed by a value but, because \pi is a constant phycical term, its value has a conventional meaning. The physical value of \pi is not the numerical value calculated as a ratio but, the physical value of \pi is its constancy under any circumstances.

A constant physical term has no physical meaning regarding its value, other than normalizing the frame of reference, therefore it has only a conventional meaning.

For instance, I can define the value of \pi to equal 1 (or eny other number) and then I need just to normalize the values of the circumference and of the values of the diameter of circles accordingly and all geometrical equations are valid, although they produce different numerical solutions. The values of the solutions for the different value of \pi are different, but when each result is compared with the respective different value of \pi, the ratio is the same. The normalized ratio results are identical for any numerical value of \pi.

This is also the case with the speed of light, according to Einstein's axiomatic definition of the constancy of the speed of light.

For my opinion, the understanding of Lorentz is a traditional physical understanding.

Einstein’s understanding can be called a structural understanding.

Einstein produced-invented a new method of "logistics" in “Physical Economics". He did not produced a new abstract theory of Physics, but he applied new mathematical and geometrical expression of Physics in order to describe the physical terms and physical phenomena. Physical terms, that was not possible to be expressed in a normalized way before Einstein’s axiomatic propositions, found the mathematical formulation to be expressed in a normalized way, because of Einstein's axiomatic constancy of speed of light.

The acceptance of this new Physical constant and its consequences in the application of mathematics and Geometry in the “language” of Physics, by Einstain, was an arbitrary action but it was not causeless. It followed the same reasoning for the introduction of the term \pi in Geometry. In Geometry, without the introduction of \pi there is no way to express one-dimension physical terms in ratio to two-dimension physical terms.

In the same context, Einstein realized that the "speed of light" is expressing a ratio between space and time that constitutes the necessary normalizing factor of the description/expression of light in a "new" scientific language that he tried to formulize.

Back to the measurement of ‘c’: Constancy or non-constancy can be measured without any reference to a measurement unit (see the Michelson experiment). And for another solution: In the Shapiro experiment a radar pulse is send to Venus and reflected back to Earth. This needs some time. Now in the moment when the sun moves close to this beam of pulses, the time is extended. The easy way to understand this is that ‘c’ is reduced in the vicinity of the sun (again without using units). - But this explanation is not acceptable by Einstein because his axiom is, that ‘c’ is always constant. So Einstein has to explain that the delay is caused by a change of the ‘space’. According to him (and his followers) we have to assume that the space close to the sun is in some way contracted, so that the photons in the pulse train have to pass a larger piece of space in order to pass the same distance as seen from outside. - And this now is the base of General Relativity as understood by Einstein.

I understand Einstein's proposition in a different way. Einstein’s explanation regarding your example is that BOTH space AND time are changing, in order for light to retain a constant speed, just a change in space is not enough (maybe you understand this also but, you forgot to write it in your message). Einstein unified the time-space realms in the same way that geometry unified the one-dimension realm and the two-dimension realm: you can not say that a circle can have different circumferences because two diameters of a specific circle circumscribe different circumference of the circle, regarding the length of the arc, by moving each diameter with different speed for the same period of time. Somehow, this is an analogy of your point of view. But "space", both in classic geometry and in Einstein’s geometry is a continuum: you can not make jumps, that is, you can not move by different “geometrical speeds”.

"Moving faster/slower" in geometrical terms means that you introduce another dimension. When a geometrical point is "moving" over the circumference of a circle on a two-dimensional space it always moves in a continuum way, therefore all points have the same “geometrical speed" and for that, they remain in the same two-dimensional realm. If a point is going to “move” faster/slower than the others, then it should do it by entering into another dimension. The geometrical speed is defined by the space/time ratio.

For instance, two diameters of the same circle that circumscribe an arc, in a two dimensional surface, from one point of the circumference to another point of the circumference, circumscribe the same space on the circumference of the circle, because the circumference is a continuum, and the diameters have to move in the same "geometrical speed". The only way to have the two diameters circumscribe different lengths of space (spaces of arc) as they move from the common starting point to the common final point is by making them move in different two-dimensional planes in a three-dimensional space, making them move over a spherical surface, starting and arriving to the intersecting points of the two-dimensional planes with the spherical surface. Then the "moves" of the diameters can be continuum with different speeds covering different space-lengths in the same time periods. This is something that can not be done in a two dimensional plane.

Thus, change of speed in a continuum “space” requires the introduction of a new dimension. This is what Einstein did by proposing and by adopting a constant “speed of light” that offers “the constancy of speed”, which is required by “space continuum”, while at the same time by introducing the dimension of time, he offered the normalizing factor in order to make possible the change of speed when the speed is measured without the dimension of time.

In the same context, your reasoning has to provide a non continuum mathematical system of physics, in order to explain how the speed of light is "reduced in the vicinity of the sun". I wonder how you might be able to overcome this requirement.

PS: Einstein’s proposal did offered a new point of view and provided the frame of using “new” mathematics in Physics in the way it was not possible to do this before. It does however have its limitations, not because it is “wrong”, but because it can not explain/express what it does not express. For these unexplained physical terms, we need to enrich our “language”, it is the way of the evolutionary process of science.


Leandros

 

[Albrecht]

Albrecht: in GR, the hypotheses of SR (including constancy of the speed of light in inertial frames) are only required to hold in sufficiently small regions of space-time.
Furthermore, the path traveled by a photon has zero (proper) length. This is true both in SR and GR.

Hurkyl: You are right if you refer to Minkowski metric. This one can - if in a gravitational field - only be applied to sufficiently small regions. If, on the other hand, you apply (following Einstein) the Remannian metric, then ‘c’ is constant independent of the size of the region, or of any motion, or of the strength of the gravitational field.

From imagination, one could conclude that the path traveled by a photon is always zero if measured in its own proper frame. But to find this result formally, one has to transform the motion with use of the Lorentz transformation into the frame of the photon. That is mathematically not permitted because it requires a division by zero. If seen from a frame at rest (or from a frame moving with any speed slower than ‘c’) the photon travels on a path with finite, non-zero length.

 

[Hurkyl]

If, on the other hand, you apply (following Einstein) the Remannian metric, then ‘c’ is constant independent of the size of the region

What do you mean by `the' Riemannian metric? There are lots of Riemann metrics, and if I recall the definition correctly, none of them are suitable for a space-time manifold.

And of course 'c' is a constant independent of the size of the region -- just like '2', 'e', and '-475 sq. in / Ampere-Coulomb' are all constants too.

So, I have no idea what you're trying to say here.

From imagination, one could conclude that the path traveled by a photon is always zero if measured in its own proper frame. But to find this result formally, one has to transform the motion with use of the Lorentz transformation into the frame of the photon.

There's no imagination involved, nor any sort of transformation. There is an integral for computing the proper distance along a worldline: \int_\gamma \, ds. If you plug the worldline of a photon into the integral, the answer is zero.

the photon travels on a path with finite, non-zero length.

It sounds like you are confusing "coordinate displacement" with proper distance.


I don't remember anymore why I brought this up. (In fact, it really doesn't even make sense at all to ask the proper distance along the path something travels -- only what the proper time along its path was... which again is zero for a photon)

 

[Albrecht]

... That means that its value may be expressed by any system of units (with the value of c, 1, or any other), because the value of the speed of light has an absolute meaning, but then all other values of variable physical terms of space-time should be expressed in relation to the defined constant absolute value of the speed of light.
...
Therefore, the physical term “space”, as a physical term that is being involved in the measurement of the speed of light as length, lost its absolute meaning as a physical constant and it is nowadays expressed by the speed of light as a variable physical term by the definition of the unit meter . Same thing happened to the physical term "time" by the definition of the unit second.

This, however, seems only to be true if we can rely, that the physical laws are as assumed by Einstein. And these laws do not only have to be true but have to be fixed in our physical world like e.g. the number \pi.

... In an analogy, this is like the relation of the circumference and of the diameter of circle. For any circle, the circumference is expressed by the diameter and at the same time the diameter is expressed by the circumference, and for all circles the ratio of the circumference to the diameter is \pi. The term \pi is expressed by a value but, because \pi is a constant phycical term, its value has a conventional meaning. The physical value of \pi is not the numerical value calculated as a ratio but, the physical value of \pi is its constancy under any circumstances.

Again, this analogy assumes that the law assumed by Einstein is not a local law in a specific context but a very fundamental law governing our physical world.

... Einstein produced-invented a new method of "logistics" in “Physical Economics". He did not produced a new abstract theory of Physics, but he applied new mathematical and geometrical expression of Physics in order to describe the physical terms and physical phenomena.

I have a little problem to understand what you mean by the term “Physical Economics". But in spite of this I agree to your consideration.
What Einstein did, is called the “geometrization of a process”. This technique to describe a physical process was invented ca. 1800. Since that time a lot of physicists and engineers have shown that almost every physical or technical process can be converted into a geometrized form. The advantage of such conversion is that the result is often mathematically very elegant. The disadvantage is that the logical causes of the process are often not visible. - Both aspects, the good and the bad one, are typical for Einstein’s description of relativity.

So, my idea is to come back to a non-geometrized version of relativity.

... Einstein’s explanation regarding your example is that BOTH space AND time are changing, in order for light to retain a constant speed, just a change in space is not enough (maybe you understand this also but, you forgot to write it in your message).

Of course you are right. I omitted the time part because I found the space part better for the imagination. But both contribute.

... In the same context, your reasoning has to provide a non continuum mathematical system of physics, in order to explain how the speed of light is "reduced in the vicinity of the sun". I wonder how you might be able to overcome this requirement.

It is possible to develop a version of relativity, which does not require Einstein’s assumptions about space-time. Regarding SR, Hendrik Lorentz has proven that a field contracts in motion. Dirac and Schroedinger have shown that an electron has an internal oscillation with ‘c’. Both assumptions are sufficient to explain SR without any use of Einstein’s space-time.

A similar development is possible for GR. The reduction of ‘c’ in a gravitational field can be explained from a QM process (i.e. the influence of the exchange particles of other forces on a light-like particle). If the reduction of ‘c’ is now explained, the contraction of fields and the dilation of clock-speed can be explained in a similar way. All known phenomena of GR can be explained in this way. To say it again: The assumption about space-time is then no longer necessary to explain the existing observations.

 

[HallsofIvy]

As mentioned before, here is a different understanding about whether contraction is a result of a measurement or a physical reality. Most physicists I know believe, that the former is true. For the opinion of Einstein the latter is true. And the latter is necessary to deduce GR from SR.

Are you really asserting that most physicists you know disagree with Einstein? And GR?

 

[Albrecht]

What do you mean by `the' Riemannian metric? There are lots of Riemann metrics, and if I recall the definition correctly, none of them are suitable for a space-time manifold.
And of course 'c' is a constant independent of the size of the region -- just like '2', 'e', and '-475 sq. in / Ampere-Coulomb' are all constants too.
So, I have no idea what you're trying to say here.

To my foregone discussion with Leandros you commented saying, that ‘c’ is only constant within a sufficiently small region. So I wanted to remind, that in Einstein’s space-time continuum c is always constant. - This is in contrast to an understanding of relativity, where ‘c’ is in truth not constant, but only the measurements of c yield always the same value.

There's no imagination involved, nor any sort of transformation. There is an integral for computing the proper distance along a worldline: \int_\gamma \, ds. If you plug the worldline of a photon into the integral, the answer is zero.

Yes, you can use this integral. But in this case 'gamma' is infinite. This is a problem (to say it cautiously) in a mathematical calculation.

I don't remember anymore why I brought this up. (In fact, it really doesn't even make sense at all to ask the proper distance along the path something travels -- only what the proper time along its path was... which again is zero for a photon)

I agree, it does not make sense. So I have wondered why you brought this into the discussion.

 

[Albrecht]

Are you really asserting that most physicists you know disagree with Einstein? And GR?

What I can see is a confusing discussion about what 'contraction' means. If I talk to other physicists about 'contraction', most of them say that contraction is a result of a measurement. Few say that contraction is real.
The actual postion of someone also depends on what the actual topic is.

For Einstein contraction was real. That is visible from the way as he developed GR from SR. Generally for GR it has (for my understanding) to be assumed that contraction is real. If it would not be so, contraction could not be used to explain e.g. the deflection of light at a center of gravity. Because in that case the photon moves - according to Einstein - along a straight line within the curved space.

 

[Hurkyl]

Yes, you can use this integral. But in this case 'gamma' is infinite. This is a problem (to say it cautiously) in a mathematical calculation.

(1) Integrating over infinite domains is generally not a problem. (Especially nonnegative things)
(2) Why would gamma be infinite?

I agree, it does not make sense. So I have wondered why you brought this into the discussion.

I remember now -- you kept talking about the coordinate distance photons would travel, but coordinate distance is an irrelevant concept. (It has absolutely no physical bearing whatsoever -- it is nothing more than the result of whatever convention we've decided to use for labelling events with 4-tuples of real numbers)

So my first thought was to bring up proper distance -- my brain hadn't quite managed to get so far as that distance is just a red herring in this context when I replied.

 

[Albrecht]

(1) Integrating over infinite domains is generally not a problem. (Especially nonnegative things)
(2) Why would gamma be infinite?

You would integrate over pieces of zero. Because every differential dx has to be divided by ‘infinite’ which is questionable.

It is the definition of gamma. For ‘v=c’ which is the case for a photon, the denominator of the definition becomes zero.

I remember now -- you kept talking about the coordinate distance photons would travel, but coordinate distance is an irrelevant concept. (It has absolutely no physical bearing whatsoever -- it is nothing more than the result of whatever convention we've decided to use for labelling events with 4-tuples of real numbers)

If you use a radar system, the photons emitted by the radar antenna travel through a certain distance. This distance is then evaluated from the travel time of the radar pulses. The resulting information indicated on the radar screen shows coordinate distances. (Formally it should be corrected for the reduction of ‘c’ in our gravitational field; but that effect is negligible).

 

[Hurkyl]

You would integrate over pieces of zero. Because every differential dx has to be divided by ‘infinite’ which is questionable.

It is the definition of gamma. For ‘v=c’ which is the case for a photon, the denominator of the definition becomes zero.

The gamma in \int_\gamma \, ds denotes the path over which we're integrating ds. It's a habit I've carried over from math classes.

If you use a radar system, the photons emitted by the radar antenna travel through a certain distance. This distance is then evaluated from the travel time of the radar pulses. The resulting information indicated on the radar screen shows coordinate distances.

Only in the coordinate chart whose coordinates are defined by the results of this experiment! It would not in any of the infinitely many other coordinate charts we might have agreed upon. (Even if we restrict ourselves to charts where the radar antenna is always at the spatial origin!)

 

[Albrecht]

The gamma in \int_\gamma \, ds denotes the path over which we're integrating ds. It's a habit I've carried over from math classes.

The normal use of gamma is as a symbol for the relativistic Lorentz factor. So I find it a bit confusing if you use it for a different purpose.

Only in the coordinate chart whose coordinates are defined by the results of this experiment! It would not in any of the infinitely many other coordinate charts we might have agreed upon. (Even if we restrict ourselves to charts where the radar antenna is always at the spatial origin!)

We humans have fortunately a common understanding what a ‘distance’ means.

You refer to the use of ‘space’ by Einstein. - We should keep in mind that Einstein’s theory uses a formalism to describe relativity called “geometrization”. The method of geometrization to describe a physical (or technical) process was invented ca. 200 years ago, that means ca. 100 years before Einstein. Einstein re-invented it. For a time it was quite much in fashion because it provides a quite elegant way for a mathematical description. On the other hand it makes the physical situation more difficult to understand.

In the meantime the use of geometrization is almost ceased because of its disadvantages. Only in the context of relativity most physicists still believe that it has to be used.

If we do not follow the geometrizing formalism, it is very clear what ‘distance’ means.

 

[AlphaNumeric]

The normal use of gamma is as a symbol for the relativistic Lorentz factor. So I find it a bit confusing if you use it for a different purpose.

It's used for many things, and in the case of integration, it's the traditional symbol for "path". True, putting gamma in like that isn't strickly proper, but given it's context it would be usual to intepret it as "path" immediately.