GRAVITATION CONSIDERED AS XEUTRAL MAGNETISM DUE TO MOTION O F ALL MATTER I N T I M E B Y A . P. MATHEWS
The following theory that gravitation is neutral magnetism, set up by motion parallel to the time axis of space-time of all matter in our universe, has a t least the merit of novelty, so far as I can find. In addition it enables the computation of the amount of gravitation of two hydrogen atoms, and also of the constant of gravitation, provided a certain velocity of motion in time be assumed. This assumed velocity is of the order of magnitude of the velocity in space of various stars, and is related in a very simple way to the velocity of light in space and also to the velocity in space of the negative end of the tube of force constituting the hydrogen atom. I t is in fact equal to the velocity of the negative electron in its orbit in hydrogen of 2 . 1 8 7 x I O * cms/secs multiplied by 2 / 4 1 3 7 . 1 ; and 1 3 7 . 1 is the ratio of the velocity of light to 2 . 1 8 7 X 108 cms/secs. While the proof that gravitation is neutral magnetism thus set up cannot be given until some independent determination of the velocity of movement of matter through space-time, or the ether, parallel with the time axis, at a rate of 3 . 7 3 6 X 10’ cms/secs shall have been obtained, yet the simplicity of the idea and the not improbable velocity assumed is certainly in its favor For the flow of time, Le., of matter through space-time parallel with the time axis, is undoubted, being perceived both objectively in every time series of events and subjectively directly by consciousness, where it appears as the succession of states of consciousness; and the velocity of 3 . 7 3 6 X 1 0 7 cms/secs, or 2 3 2 miles per second, is less than the velocity in space recently ascribed by astronomers to distant island universes; that velocity being of the order of 1 0 8 cms/secs. I t is of the order of magnitude of the motion of Betelgeuse, which is about 80 miles per second. There is, therefore, nothing improbable in the assumption as to the rate of motion in time. All matter, so far as known, is moving in time with an unknown velocity, vt, and is composed of hydrogen atoms. Most of these hydrogen atoms have been condensed to make more complex atoms. Each hydrogen atom, condensed and uncondensed, is an electrical di-pole, and so may be considered to be a unit of neutral, material electricity. Thus each mass of matter in the universe is a current of neutral electricity. All such currents are flowing in the same direction, in paths parallel to the time axis, and they are abreast in time. Such currents of ordinary electricity are known to attract each other if they be of the same sign. All neutral currents are of the same sign. Such neutral currents are known to attract each other. The attraction may be regarded as neutral magnetism. I t is called gravitation.
GRAVITATION CONSIDERED AS NEUTRAL MAGNETISM
I739
Since each hydrogen atom consists of two electrons, one positive and one negative, each carrying 4.774 x 10-10 electrostatic units of positive or negative charge, we may regard these electrons as half units of neutral electricity, so that each hydrogen atom is, or carries, 4.774 X 1 0 - l ~electrostatic units of neutral, material electricity. The translational motion of a charge, whether positive or negative, in space-time produces magnetism. The magnetism is polar, or dissymmetrical, if the two ends of the neutral charge or tube of force, the positive and negative charges, move in space a t different rates; as, for example, when the negative moves about the positive in a hydrogen atom, or when the negative flows along a wire; but it is non-polar, or symmetrical, or neutral, if the two ends of the tube of force connecting the positive and negative electrons move at the same rate. Movement of a hydrogen atom as a whole in space does not set up ordinary, or polar, magnetism; but it must set up magnetism of some kind, since all motion of a charge, whether positive or negative, is known to set up magnetism. It is the peculiarity of gravitation that it is a neutral force. I t is non-polar. It is neither positive nor negative, as is electrostatic force; nor is it north and south, as is ordinary magnetism. The force of polar magnetism between two poles, north and south, or between two parallel currents of ordinary (positive or negative) electricity, is dependent upon the magnetic polarity of any material substance interposed between the poles or currents. It depends upon the magnetic permeability, p, of that material. Non-polar, or neutral magnetism, would not , presumably, be at all affected by the interposition of matter; so far, at least, as either the magnetic or electrical polarity of that interposed matter is concerned. Corresponding with this expectation, gravitation is known to be independent both of the magnetic permeability and the specific inductive capacity of any matter interposed between gravitating masses. Kow if each condensed hydrogen atom, making a part of other atoms and carrying 4.774 X 1 0 - l ~electrostatic units of neutral electricity, by its motion in space generates neutral magnetism in the same manner and to the same degree as an equal quantity of negative or positive electricity, two hydrogen atoms of neutral charge, e, moving in parallel paths, abreast, and at a velocity of v, in space, at a distance, d, apart, would act upon each other magnetically (attract) with a force expressed by the formula: (1)
Me2/d2X v,Z dynes,
when e is expressed in electromagnetic units; d in centimeters; and v,, the velocity parallel to a space axis, in cms/secs. Expressing this in electrostatic units we have: (2)
e2/Kd2 X ?/c2
x
v,2/1? dynes.
In formula ( 2 ) the numeral, one, represents unit velocity; Le., one centimeter per second. Two hydrogen atoms moving abreast in parallel paths in space with unit velocity a t unit distance and in the same direction should, therefore, if this
I740
A. P. MATHEWS
formula be correct, attract each other with the same magnetic force as two electrons' similarly moving, a force of (4.774 x 10-'~)~/(3x 1 0 ~dynes, ~ ) ~ or 2.28 X IO-'^/(^ X iozo), or 2.533 X I O - ~ O dynes. And if they move in space in parallel paths with a velocity, c, that of light, then such atoms would attract with a force of 2.28 X IO+ dynes, at unit distance, provided that this formula holds at such extreme velocities. It hardly seems possible that the gravitational force between two hydrogen atoms due to their parallel motion in space can be as large as this. But on the other hand it is known that the mass of an electron does increase with the velocity of space motion, and directly as c / d @ - v2); and also by the Newtonian law the gravitational force is a function of the mass. So that it is not improbable that the gravitational force would vary with space velocity as this formula states. If the mass increase with the velocity in the manner supposed by relativity, then formula (2) would need a correction which becomes of material importance only when the velocity comes very close to that of light, since the mass is supposed to become infinite a t that velocity. The correction would be of the form I / ( I - v2/c?). So that the corrected formula should be: (3 1
or, (4)
e2/Kd2 X
I ~ / CX ~
x c2/(c? - v.2); - v,2) dynes.
v.2/1?
e2/Kd2X v.l/(c2
Whether gravitational attraction does vary with the velocity in space according to this formula, I do not know; but the corresponding formula for the velocity in time appears to give the correct result. Of course movement in space can hardly be the cause of gravitation as we know it since the various masses of matter are moving in all directions in space. But in time they are all moving at the same rate, in the same direction, in parallel paths. The formula will be changed in one particular if the velocity of motion be not motion in space but motion in time. It is obvious, since a velocity is the ratio of the number of units of space extension traversed by the moving body to the number of units of time endured, that if we increase the component of the velocity parallel with the time axis we accomplish the same result as if we retarded the velocity of motion parallel with the space axis. Any increase in speed of motion parallel with the time axis appears to retard the velocity in space; and any decrease in motion parallel with the time axis appears to accelerate the motion in space; and vice versa, velocity in time appears to increase when velocity in space is diminished. This being so the force must vary inversely with the square of the time velocity, if it vary directly with the square of the space velocity. The mass of a body must be an inverse function of the velocity of its movement in time, if it be a direct function of its velocity in space. Expressing, now, formula ( 2 ) in terms of time velocity, v,, we have: (5)
e?/Kd? X
I?/c?
X
I ~ / v dynes ~?
Of c o u r e the electvostatm force of repulsion between two electrons overbalances this
magnetic force; but such repulsion
18 absent
between neutral charges.
GRAVITATION COXSIDERED AS XEUTRAL MAGSETISM
1741
Since the polar force of attraction of magnetism, the ordinary form, varies directly as the square of velocity in space it must be inversely as the square of the velocity in time. And if gravitation be neutral magnetism set up by the symmetrical motion in time of the tube of force, which is the atom, then gravitation must follow this same law. If it were corrected for the variation of mass with velocity we would have as the corrected formula: (6) (i)
e2/Kd2 X
I~/C*
X I ~ / v >X (c’ - vtz)/c2dynes; or,
e2/Kd2 X (cz - vt2)/c4vt2X
dynes.
If we suppose that the velocity of the flow of time through matter in our universe, or the velocity of motion of matter parallel to a time axis of spacetime, be at the same rate as the velocity of the negative electron moving in space about the positive center in the hydrogen atom, in Bohr’s first orbit, or 2.187 X 108 cms/secs, this formula would give for the gravitational attraction of two condensed hydrogen atoms (atomic weight unity) at one centimeter distance (4.774 X 10-’O)~/(3 X IOIO X 2.187 X 1 0 ~or) ~5 . 2 9 5 X IO-”’ dynes. This result is not far from being correct. In fact it is precisely 4/137.1 times the correct figure. For since two one gram masses of matter more complex than hydrogen atoms at unit distance attract gravitationally with the force of 6.670 X IO@ dynes, according to Heyl’s recent careful determination, and there are, in a mass of one gram of material composed of atoms more complex than hydrogen, 6.061 x 1 0 2 3 condensed hydrogen atoms, each pair of such atoms of hydrogen must attract a t unit distance with the force of 6.670 X 10-~/(6.061 X 1 0 ~dynes. ~ ) ~ This is 1.815 X IO-^^ dynes. This is 13j.1/4 times j.295 X 10-57 dynes which the formula gives when assuming the motion to be 2.187 x 108 cms/secs. It is clear from this that gravitation may be regarded as neutral magnetism set up by the translational motion of all matter parallel with the time axis. I t is neutral because both ends of the tube of force are moving with the same velocity in time. The positive electron in the atom is moving in time a t the same velocity as the negative. From formula ( 5 ) we may calculate what that velocity is. I t is 3 . 7 3 6 X 10’ cms/secs. This gives an exact result. This velocity is (2.187 X I O ~ ) / ( ~ ~ /And Z ) 137.1 . is (3 X lolO)/z 187 X 10~). I t is also 135 X 1.007 76’. We may secure further evidence that this is correct. I have shown elsewhere how easily a hydrogen atom may be regarded as a very short light pulse which has been absorbed by the ether, becoming thus protohydrogen, and afterwards partly dissociated to form hydrogen by the absorption of a second pulse having twice the frequency of a Rydberg pulse. The first, or creative, light pulse, of a wave length of about I .7 j X I 0-14 cms, is supposed to be moving parallel with the time axis. As long as it moves with the velocity of light it has hc/za erg-centimeters in it. This is the quantity, then, of the pulse before absorption. The gravitational attraction of two pulses thus moving in time with velocity of light will be zero, according to formula (7).
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A. P. MATHEWS
But if the pulses be reduced in velocity by absorption then they will attract each other. And at a distance of L between them, when moving with a velocity, vt, or 2.187 X 108cms/secs, the formula: hc/zaL2 X 1 ~ / 4 c ~dynes v~~
(8)
gives, at I centimeter for L, the correct force of attraction of 1.815 x 10-55 dynes. Here again represents unit velocity to the fourth power. If, however, we consider the amount of erg-centimeters after absorption, in the atom itself, to be hv’./2~, where v‘. is the velocity of the negative electron in space, or 2.187 X 108cms/secs, then the formula hv’,/2nL2X I ~ / c * v ~ ? gives the correct value of 1.81j X IO-^: dynes for the attraction of the two atoms at unit distance, when vt, the velocity in time, is 3.736 x I O ? cms/secs, the value already found; h is 6.547 X IO-*? erg-secs, and cis 3 X IOIO cms/secs; L is of course unity. This is the same formula as (5) since hv’,/zx is precisely equal to e*/K. The gravitational attraction of two one-gram masses at a distance, d, apart, where the neutral charge, e, on each hydrogen atom is 4.774 x 10-10 e.s.u. will be: (6.061 X 10*~)* X e2/Kd2 X
(9)
I ~ / C ~ Vdynes. ~*
And for any two masses of n and n’ grams respectively it will be: nn‘ (6.061 X
(10)
1oZ3)* X
e2/Kd2 X I ~ / c ? v dynes. ~*
This is the Newtonian law of gravitation; since (6.061 X 1oZ3)*X e*/K x I ~ / c is ~ the v ~ numerical ~ value of the gravitational constant, k. If it be corrected, as in formula (7) for velocities approaching the velocity of light, it would be, more correctly, : (11)
nn’ (6.061 X 1oZ3)*X e*/Kd* X I ~ ( c *- vt?)/c4vt*dynes.
The velocity is of course the velocity in time rather than in space. Since formula (7) gives the gravitational attraction of two condensed hydrogen atoms in other terms than MM’k/d2, we may easily find the value of the gravitational constant, k, of the Newtonian law. If m H ris the mass of a condensed hydrogen atom and equal to 1.663 X 10-~‘/1.00;76 grams, the value of k will be: k = e2/Km2HtX 14/c2vt*dynes+ velocity4
(12) =
(4.774 X
IO-~O)~
X 3.736 X =
6.670 X
IO-?
X 1.00;76*/(1.663 X IO-*^ X 3 X
I O ~ O
10’)~
dynes-’ vel4
=
6.670
x
IO-*
(L3)/(1MT’)
We may conclude from this examination of the problem that gravitation may very well be a non-polar, or neutral, magnetic force, set up by the equal motion of both poles of the electric tubes of force constituting all matter. The motion is parallel with the time axis, so that all masses of matter con-
GRAVITATIOS CONSIDERED A S NEUTRAL MAGNETISM
1743
stitute parallel currents of neutral electricity; and the velocity of such movement of matter in our universe is at the rate of 3 . 7 3 6 X 10’cms/secs. This velocity may not be the same in other universes. If it vary from this figure the mass of the hydrogen atom and all other atoms would vary also somewhat and presumably the spectral lines of such atoms would be shifted slightly from their position as known to us. Since motion in space seems to have the opposite effect to motion in time, producing energy in place of inertia, it may very well be that all matter repels other matter gravitationally in time, just as it appears to attract it in space. Accordingly all matter would appear to tend to distribute itself uniformly in time; while it tends to aggregate in space. So far as we know a t present, matter is distributed, on the whole, uniformly in time, there being neither increase nor decrease in the total quantity of matter as time progresses. University of Cinnnnati.
