Relativity is broken"Relativity Broken: Uncovering the Mystery

[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.