Relativity and the Problem of Space (Part 13)

LCDM

Reference: http://www.relativitybook.com/resources/Einstein_space.html

NOTE: Einstein’s statements are in italics. My understanding follows in bold.

“Generalized Theory of Gravitation

“The theory of the pure gravitational field on the basis of the general theory of relativity is therefore readily obtainable, because we may be confident that the “field-free” Minkowski space with its metric in conformity with (1) must satisfy the general laws of field. From this special case the law of gravitation follows by a generalisation which is practically free from arbitrariness.

“The further development of the theory is not so unequivocally determined by the general principle of relativity; it has been attempted in various directions during the last few decades. It is common to all these attempts, to conceive physical reality as a field, and moreover, one which is a generalisation of the gravitational field, and in which the field law is a generalisation of the law for the pure gravitational field. After long probing I believe that I have now found  the most natural form for this generalisation, but I have not yet been able to find out whether this generalised law can stand up against the facts of experience.

“The question of the particular field law is secondary in the preceding general considerations. At the present time, the main question is whether a field theory of the kind here contemplated can lead to the goal at all. By this is meant a theory which describes exhaustively physical reality, including four-dimensional space, by a field. The present-day generation of physicists is inclined to answer this question in the negative. In conformity with the present form of the quantum theory, it believes that the state of a system cannot be specified directly, but only in an indirect way by a statement of the statistics of the results of measurement attainable on the system. The conviction prevails that the experimentally assured duality of nature (corpuscular and wave structure) can be realised only by such a weakening of the concept of reality. I think that such a far-reaching theoretical renunciation is not for the present justified by our actual knowledge, and that one should not desist from pursuing to the end the path of the relativistic field theory.” ~ Albert Einstein

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Reference:  Disturbance Theory of Space

Time enters into picture with the disturbance of space. This disturbance seems like a wave with the attributes of wavelength, period and frequency. We may visualize space and time as having boundaries imposed by wavelength and period. Space and time keep up a constant ratio of “c”.

We may define space-time as chunks of wavelength-period, across which we have continuity. Frequency is inversely proportional to wavelength and period. In the regions of low-frequency the chunks of space-time are larger than in the regions of high-frequency. Thus we may postulate space-time having a “density” that increases as the disturbance increases.

This density of space-time is uniform in the regions of uniform disturbance. As disturbance increases or decreases, the space-time density also increases or decreases  A gravitational field appears in areas where space-time density is changing.

Mass may appear in those regions of space-time where gradient of change in space-time density is very high. This is more likely to appear in the regions of high densities.

An interesting view arises with respect to the regions being studied by quantum mechanics. The idea of location in space shall depend on density of space-time. Only in the regions of mass (very high densities) could a location be approximated by a dimensionless Euclidean point. This approximation may not apply to the electronic region of an atom. 

In this light we need to re-examine the Heisenberg’s uncertainty principle.

Previous: Relativity and the Problem of Space (Part 12)
Next:  Relativity and Problem of Space

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Comments

  • vinaire  On November 22, 2015 at 10:16 PM

    The Heisenberg’s uncertainty principle applies to complementary properties of a particle. The term that is not well-defined here is “particle”.

    So the uncertainty is actually associated with the definition of “particle”.
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  • vinaire  On November 22, 2015 at 10:20 PM

    1. Mathematically, a classical particle is defined by a point in a 6 dimensional phase space.
    2. A particle is a thing that has position and momentum and nothing else.
    3. Physically, classical particles are used when the internal extent of the object is too small to be relevant on the scale you’re looking at.
    4. Quantum mechanically things get more complicated.
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  • vinaire  On November 22, 2015 at 10:23 PM

    A “particle” seems to be further abstraction of “material point”. A material point always has a center of mass. In fact the coordinates of a particle are synonymous with the center of mass of the particle.

    When we talk about a location in an electromagnetic field, I do not think it can be described by a precise set of coordinates because there is no material point or a center of mass to pinpoint it. That seems to be the case with locations of “electrons inside an atom”. An “electron inside an atom” as a particle is just a conjecture because there is no center of mass there, which goes around the nucleus. An “electron outside the atom” may exist as a particle with a center of mass, but I haven’t seen that expressesd explicitly.

    The same consideration seems to apply to a location in space when there is no material point or center of mass involved. There is no “empty space” according to Einstein. When there is no matter, then there is just a field present. So, when we are talking about locations in space we need to define them the way we define locations in a field.

    We cannot specify locations in a field in terms of dimensionless Euclidean points, or can we?

  • vinaire  On November 22, 2015 at 10:29 PM

    All fields exist at all points in time and space.

    A field is disturbed space. Time is an aspect of disturbance.

    The Higgs Field seems to be just the “hypothetical undisturbed space” that forms the background of disturbed space. The disturbed space appears in the form of field and mass.
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  • vinaire  On November 23, 2015 at 11:08 AM

    Quantum (Physics)

    1. the smallest quantity of radiant energy, equal to Planck’s constant times the frequency of the associated radiation.

    2. the fundamental unit of a quantized physical magnitude, as angular momentum.
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  • vinaire  On November 23, 2015 at 11:24 AM

    All elementary particles are merely excited states (or quanta) of some field. This includes

    • The Higgs boson, which is the quanta of the Higgs field,
    • The photon, which is the quanta of the electromagnetic field,
    • The electron, which is the quanta of the electron field, and so on.

    That means quanta are points of convergence and condensation of disturbance. Mass comes from condensation points in the field.
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  • vinaire  On November 23, 2015 at 11:26 AM

    Fields may couple to other fields, and in this case the fields are said to be interacting with one another.

    This means the various disturbances interact with one another.

  • vinaire  On November 23, 2015 at 11:41 AM

    When space is disturbed it breaks into electric and magnetic fields. This could be what is known as spontaneous symmetry breaking. When this disturbed space converges and condenses we get mass.

  • vinaire  On November 23, 2015 at 8:34 PM

    (1) The “Disturbance field” provides condition of space-time at each location. Electromagnetic and Gravitation fields shall be aspects of the Disturbance field.

    (2) The condition of space-time can be very complex and may evolve in many different ways. It may evolve into charged and mass particles.

    (3) We assume charged and mass particles as the source of respective fields, but the reverse seems to be true. These particles are generated within the field.

    (4) “Disturbance field” comes about with disturbance of space. The disturbance seems to come from some restoring inertial force of cosmic nature.
    .

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