**Abstract**

By introducing virtual 4th dimension to represent time in similar manner like 3 dimensions of space which can be measure in terms of length, the attempt is made to explain how velocity of the object in “Special Theory of Relativity” causes time dilation and how matter affects time in case of “General Theory of Relativity”. Same concept has been used to solve the “Galaxy Rotation Curve” problem and pioneer anomaly without need of any dark matter. Finally, it is shown that, increase in time affects gravity giving new definition to gravity based on which explosion of black hole and evolution of Universe is predicted.

Keywords: Galaxy Rotation Curve, Dark Matter, Special and General Theory of Relativity.

**Introduction**

Our Universe is made of 3 dimensional space and one dimensional time (atleast these are the dimensions which are directly affecting to us in our day to day life and are not hidden like those remaining 7 dimensions in case of string theory). As per special and general theory of relativity, these 3 dimensional space and time are not two separate things, but are closely connected to each other. Hence, instead of measuring time in terms of unit of second, by introducing virtual 4th dimension, we can represent time in terms of measuring unit – meter such that one second equal to 3*108 meter.

**Time Dilation in Special Theory of Relativity**

In following figure, the 3 dimensional space is considered as 2 dimensional sheet moving in remaining vertical virtual dimension at the speed of light, (c= 3 * 108 m) for mass less (energy) particles like photons. In real Universe, the vertical dimension shown in figure is not as like dimensions of the space having length, but it is an imaginary dimension. Here, for simplicity, it is assumed that the vertical dimension representing time is similar to dimensions of space having length as measuring quantity so that 1 second in vertical dimension is equivalent to 3* 108 m. In other words, 3 Dimensional Space is moving in 4th Dimension at the speed equal to speed of light for mass less particles like photon.

Figure – 1.0

The above concept very well explains why particles like photons can travel at speed of light? It is a mass less particle which do not affect space-time geometry. Also, from figure it is seen that, for photon which is travelling at the speed of the light, its time from the frame of reference of the stationary object should be equal to zero i.e vertical distance measured in above figure should be zero. In other words, photon or energy particles should entirely live only in 3 Dimensional space. For the object having velocity less than the speed of light, the vertical distance or time can be calculated as shown in following figure.

Figure – 2.0

In above figure, when the object is at stationary (V=0), the vertical dimension will always measure the distance equal to 3 * 108 m in 1 second. But, if the same object travels at velocity ‘V’, then, in one second, the vertical distance will measure [c*Sqrt{1-(V2/c2)}] m, because, the path of the object no longer remain perpendicular to our 2 Dimensional sheet but remains in inclined direction as shown in figure -2. Therefore, time of the moving object will always remain less than time in reference frame of stationary object or time is slowed down with increase in velocity ‘V of the object which is nothing but “Time Dilation” phenomenon in “Special Theory of Relativity”. Also, for moving object, time get slow down and not for the stationary object, hence, twin paradox will never happen. It is something like every object (moving as well as stationary) always remains attached with fixed or absolute frame of reference in their frame of reference. It means, the moving as well as stationary object in their respective frame of reference will always measure one second equal to 3* 108m in above figure. For stationary object, time and space never mixed with each other or remains as separate entities, while for moving object, its velocity V in space affects its time or vertical distance measured in virtual dimension.

**Time Dilation in General Theory of Relativity**

As per General Theory of Relativity, matter bends space-time making curvature of space-time around it giving effect of gravity and this curvature depends upon quantity of matter. More matter, more will be curvature of space-time. This concept usually demonstrated by scientists as the heavy object kept in middle of 2 dimensional rubber sheet representing fabric of 3 dimensional space which bends the rubber sheet due to its weight. When another light object is moved from edge of rubber sheet towards the heavy object, it got trapped in curvature (gravity effect) made by heavy object and follow inward spiral trajectory around this heavy object such that its velocity increases with decrease in distance from the heavy object. Finally, it collapsed into heavy object. Thus, in this demonstration, curvature of rubber sheet due to presence of heavy object very well explains gravity effect according to General Theory of Relativity. But, there is one hidden thing in above demonstration that is, in order to produce curvature effect on rubber sheet due to weight of heavy object, it requires additional force in remaining 3rd dimension (perpendicular to 2 dimensional rubber sheet) which is nothing but gravitational force produced by the Earth. For example, if same demonstration is done on the moon, the curvature produced by heavy object will become less than that on the Earth because gravitational strength of the Earth is six times greater than the moon. Now, Einstein is on right track with respect to his General Theory of Relativity which has been already confirmed through number of experiments like bending of light, mercury perihelion, gravitational lensing etc. It suggests that in order to produce effect of curvature of space-time, matter must have to produce force in the vertical virtual dimension so that this force causes the matter to move in opposite direction of flow of time. In other words, the object due to presence of its matter always moves in opposite direction with respect to direction of flow of time. It can be explained in the following figure:

Figure – 3.0

From above, it is clear that presence of matter bends space-time slowing down time such that time near surface of the object is always less than away from it. But as already told, the vertical dimension is a virtual dimension representing time for our sake of simplicity, in real universe, instead of bending of space in time or virtual vertical dimension, it remains as flat 2 dimensional sheet such that its density become higher near the surface of the object which decreases as moving away from the object. Or space-time is not empty but filled with medium having its own density representing flat space-time which can be called as vacuum density. Thus, presence of matter causes increase in vacuum density near the object which decreases while going away from the object and finally become constant to represent flat space-time. But, if gravitational constant, G is really a constant, then curvature of space-time in above figure should not changed with increase in time difference, ?T because of increase in time itself. This can be achieved by keeping restriction on gravitational strength (acceleration) due to Gravitational Constant, G up to specified region such that beyond this region effect of G on gravitational strength become very negligible and it entirely depends upon increase in time i.e. changes in curvature of space-time is more beyond this region. The equation for gravitational strength can be written as:

g = (G*M/r2)*{1+ (3P/?c2)} – f(T) = a – f(T) — (1)

-Ve sign indicates that spreading of curvature of space-time radially out. In other words, the force due to f(T) acts like repulsive force or opposite to attractive gravitational force.

Where, g = Gravitational strength or acceleration, G = Gravitational constant = 6.67*10-11 m3/(Kg*Sec2);

M = Mass of the object creating gravitational field, r= distance from the center of the object, and

f(T) = Function of Time which acts opposite to gravitational strength.

From above eq., for f(T) very less than a, G dominates the gravitational strength and as a becomes very less than f(T) because of inverse square relationship with r, g must be expressed in terms of f(T). Note that value of G always remains constant and changes in curvature of space-time is governed by f(T) beyond the region from where effect of G becomes negligible while effect of increase in time dominates beyond this region.

The above analysis can be well illustrated in following figure;

Figure – 4.0

From above figure, the region for which value of a<

Figure – 5.0

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). The discrepancy between the curves is attributed to dark matter.

In 1959, Louise Volders demonstrated that spiral galaxy M33 does not spin as expected according to Keplerian dynamics, a result which was extended to many other spiral galaxies during the seventies. Based on this model, matter (such as stars and gas) in the disk portion of a spiral should orbit the center of the galaxy similar to the way in which planets in the solar system orbit the sun, that is, according to Newtonian mechanics. Based on this, it would be expected that the average orbital speed of an object at a specified distance away from the majority of the mass distribution would decrease inversely with the square root of the radius of the orbit (the dashed line in Fig. 1). At the time of the discovery of the discrepancy, it was thought that most of the mass of the galaxy had to be in the galactic bulge, near the center. Observations of the rotation curve of spirals, however, do not bear this out. Rather, the curves do not decrease in the expected inverse square root relationship but are “flat” – outside of the central bulge the speed is nearly a constant (the solid line Fig. 1). The explanation that requires the least adjustment to the physical laws of the universe is that there is a substantial amount of matter far from the center of the galaxy that is not emitting light in the mass-to-light ratio of the central bulge. This extra mass is proposed by astronomers to be due to dark matter within the galactic halo, the existence of which was first posited by Fritz Zwicky some 40 years earlier in his studies of the masses of galaxy clusters.

The introduction of dark matter in galaxy rotation curve is actually our lack of understanding of gravity i.e. how gravity works. From above equation (3), it is seen that for region where a<

Pioneer anomaly or Pioneer effect is the observed deviation from predicted trajectories and velocities of various unmanned spacecraft visiting the outer solar system, most notably Pioneer 10 and Pioneer 11. Pioneer 10 and 11 were sent on missions to Jupiter and Jupiter/Saturn respectively. Relatively simple, the spacecraft were spin-stabilised in order to keep their main antennas pointed towards Earth using gyroscopic forces. Although the spacecraft included thrusters, these were left unused after their primary encounters, leaving them on a long “cruise” phase through the outer solar system. Pioneer 10 sent back radio information about its location until January 2003, when it was about 80 times farther from the Sun than the Earth is. Pioneer 11 sent back signals until September 1995, when its distance from the Sun was about 45 times the Earth’s. But, the calculated position of the Pioneers did not agree with measurements based on timing the return of the radio signals being sent back from the spacecraft. These consistently showed that both spacecraft were closer to the inner solar system than they should be, by thousands of kilometers – small compared to their distance from the Sun, but still statistically significant. This apparent discrepancy grew over time as the measurements were repeated, suggesting that whatever was causing the anomaly was still acting on the spacecraft. As the anomaly was growing, it appeared that the spacecraft were moving more slowly than expected. Direct measurements of the spacecraft’s speed using the Doppler Effect demonstrated the same thing: the Pioneers were slowing down more than expected. When all known forces acting on the spacecraft are taken into consideration, a very small but unexplained force remains. It appears to cause a constant sunward acceleration of (8.74 ± 1.33) × 10?10 m/s2 for both spacecraft. If the positions of the spacecraft are predicted one year in advance based on measured velocity and known forces (mostly gravity), they are actually found to be some 400 km closer to the sun at the end of the year. Let us solve this anomaly by using the above concept. Assuming that, while calculating this anomaly, the first part of gravitational acceleration (G*M/R2) must be considered already, we will consider only remaining gravitational acceleration i.e f(T).

The distance by which the pioneers will be found closer to the sun at the end of the year equals to;

S= 0.5* f(T)* t2 = 0.5*3*108*2.667*10-18*(3.16*107)2

? 399 Km — (H=2.667*10-18 Sec-1 or T?12 billion years)

Which is closer to the experimental value obtained (400 Km). One more important point, here is that even at a distance of 80 A.U., f(T)<< a shows that the planetary system of our Sun should follow decrease rotation curve or velocity of planet should decrease with square root of its distance from the Sun. The planets at this distance (Approx. 80 A.U.) do not show same type of anomaly because the gravitational acceleration, a produced because of the matter of the sun is exactly balanced by centrifugal force of the planets and same is not balanced here in case of pioneers, hence anomaly exists in case of pioneers. But, because of anti-gravity effect of f(T), planets should have to move slowly away from the sun and the speed at which the planets which are moving away from the sun at this distance, is-
? = H*r = 2.667*10-18*80*1.496*1011 = 3.2*10-5 m/Sec or approx. 1Km per year.
For our earth, this velocity ? comes to be equal to 4*10-7 m/Sec or approx. 12.6 m per year.
Let us calculate, the distance by which moon should move away from the earth in one year due to effect of f(T) –
? = H* r = 2.667*10-18*3.84*108 = 10.24*10-10 m/Sec or approx. 3.25 cm per year. The current rate at which the Earth day is increasing is 0.0018 seconds/century. The semi-major axis of the lunar orbit is increasing by 3.8 centimeters/year according to laser ranging measurements made since the 1970's using the Apollo 'corner cube reflectors' deposited on the surface by the astronauts. The difference between calculated value and experimental value is due to approx. value of H which is not equal to Hubble’s constant as the moon is moving in opposite direction of flow of time increasing value of H greater than Hubble’s constant. **Dark Energy and Dark Matter**

Einstein’s General theory of relativity works very well for planets, stars even galaxies but not at larger distances comparable to size of the Universe (Ru ? 1027 m) as well as for objects like black holes and for big bang event. Then, whether really we require another theory to explain these things i.e. required to throw such a beautiful and consistent theory even though theory has been tested experimentally correct. One of the basic logical concepts is that new theory should not throw old theories which tested experimentally but should be modification of old theory to accommodate the old theory in this new theory when parameters in theory are constrained. For e.g special theory of relativity shows Newton’s basic laws of equation for v<

r = (2*G*M/c2) — (9)

Which is nothing but, Schrodinger’s radius related to event horizon of the black hole. That is our early Universe was similar to black hole except it was expanding due to creation of opposite sign of matter-energy at the edge of the Universe having its density related to increase in time. For e.g. at time T equal to 1/c or 0.333*10-8 Second, the value of r was equal to 1 m which gives M equals to 0.6746*1027 Kg from equation (9) or matter density roughly equals to 0.6747*1027 Kg/m3. With same density, the creation of opposite sign of energy was happening at same time at the edge of the Universe adding more and more matter-energy into the Universe which slowing down time or increasing value of H and thus expanding the Universe. With increase in time, f(T)>>a, at certain point, energy inside the Universe (Big black hole) must have to explode, expanding the Universe, it got escape from event horizon from which the Universe comes into existence what we are seeing right now. Still right now, the Universe is producing opposite sign of pair of energy particles at it’s the edge which density can be calculated as-

T= 13.5 Billion years = 13.5*109*3.16*107 Second = 0.426*1018 Second

r = c*T = 3*108*0.426*1018 = 0.128*1027 meter

Putting above value of r into equation (9), we get

M= (0.128*1027*3*1016)/ (2*6.67*10-11) = 0.086*1054 Kg

Which gives matter density equals to {M/(4/3*?*r3)}, 9.8*10-27 Kg/m3. In other words, right now, after 13.5 billion years after birth of the Universe, pairs of opposite sign of energy particles must be producing at the edge of the Universe having matter density equals to 9.8*10-27 Kg/m3. It is nothing but the current vacuum matter density which agrees very well with observed value.

Let us calculate how much amount of matter; the Universe must be creating per second at this moment.

dV=Increase in Volume of the Universe per second=4*?*{(R2)3-(R1)3}/3.

Where, R1=0.128*1027 m and R2-R1=3*108 m

dV=4*?*(R2-R1)*{(R2)2+R2*R1+(R1)2}/3=4*?*3*108*3*(0.128*1027)2/3 — R2?R1

=61.76*1060 m3

Increase in Matter of the Universe per Second=9.8*10-27*61.76*1060 = 0.605*1036 Kg — (10)

From above it is seen that, really, “Size does Matter”; i.e., larger the size of the Universe, greater is the creation of matter per second. Our Universe can be defined precisely as “a Big Black Hole expanding at its edge”. As there is basic natural force acting opposite to gravity force on every matter including a black hole, hence, condition of black hole will never approached towards singularity. This force increases because of gravitational force itself which causes slow down of time due to increase in matter-energy density or increase in curvature of space-time. These two opposite forces balanced each other at the condition where all matter converts into energy inside a black hole which finally moves at constant velocity, c, speed of light in downward direction or opposite to the direction of flow of time, ?T=c second for increase in time of 1 second in virtual vertical dimension as shown in figure (3) avoiding singularity condition as well as creating opposite sign of particles of energy at event horizon having matter density equals to {MB/(4/3*?*r3)}where, MB = mass of black hole and r = radius of event horizon. But, if MB remains constant or with no addition of matter inside a black hole, there will be no change in the value of r as per equation (9). In other words, gravitational force, a, should remains as a constant. While f(T) should go on to increase as black hole is moving at constant velocity c, but in opposite to the direction of flow of time which will continuously increase the value of ?T in figure 3.0 or indirectly increasing the value of H. Situation will occur when increase in f(T), repulsive force becomes greater than gravity force and at one stage with great explosion, black hole should have to spread out its entire energy into the Universe back again i.e. “Black Hole must have to Explode releasing all its Energy into the Universe.”

Fate of Universe depends entirely upon only one parameter i.e. creation of pairs of opposite sign of energy particles at edge of the Universe. As there is nothing to prevent this creation at its edge, the Universe must have to expand forever. During this time, all galaxies will move away too much farther away from each other and finally explode because of explosion of black hole situated at center of the every galaxy releasing all their matter in terms of energy into the Universe leaving the Universe with more radiations than matter. This will obviously cause decrease in value of f(T) balancing with ‘a’ because little matter was left to move in opposite direction of flow of time. But, with increase in time, there is further decrease in the value of f(T) will take place. On the other hand, M (total matter in the Universe=total energy of the Universe/c2) should increase with increase in radius i.e. gravitational strength become directly proportional to increase in radius, as shown below –

a = (G*M/r2)*{1+ (3P/?c2)} = (G*M/r2)*2 — {(3P/?c2) = 1 for radiations}

= (2*G*?v*dV)/r2

{?v = Vacuum Density, Kg/m3 remains as constant because of negligible change in its value}

= [2*G*?v*{4*?*(R2-R1)*{(R2)2+R2*R1+ (R1)2}/3}]/R12

{R1 = Size of the Universe when a=f(T) and R2 = Increase in size of the Universe after this time}

= [2*G*?v*{4*?*(R2-R1)*3*(R1)2/3}]/ R12 — R2?R1

a = [2*G*?v*4*?*(R2-R1)] ? (R2-R1)

With a>>f(T), the Universe should start to collapse until a=f(T), but time will never reverse its direction and hence space at the edge of the Universe should have to expand by creation of energy particles. From where due to increase in energy density inside the Universe because of collapsing due to gravity effect, the time should again start to slow down or at certain point energy which start to compressed will act like giant black hole moving in opposite direction of flow of time with velocity, c increasing value of f(T) such that a<

Change in Entropy is related to disorder which always increases with increase in time. Hence, with decrease or slow down in time due to gravity effect, change in entropy or disorder must have to decrease. In case of black hole, as it moves with speed of light and opposite to direction of flow of time in vertical virtual dimension as mentioned in figure 3.0, change in time for black hole becomes equal to zero or clock stops completely. Note that, still black hole has plenty of room (around 13.5 billion years) to move in downward direction in virtual dimension and hence black hole will never reach to a point of singularity. Now, because of no change in time for black hole, its entropy should remain as constant value i.e entropy should not change or disorder should not increase. In other words, the object which falls into black hole with certain entropy or disorder after crossing event horizon should have to add that entropy to the black hole without further change in entropy of the object so that entropy in black hole after addition must have to conserve. As entropy is also related to information such that increase in entropy is related to increase in information, in black hole the information should not loss because of conservation of entropy inside the black hole which will come out from the black hole itself when it will explode. The conservation of entropy is equivalent to conservation of energy {dS = Change in Entropy = (Change in Energy/ Absolute Temperature)}. As proved earlier, black hole is a giant energy or mass less object just like photon, both are travelling with speed of light with only difference between photon and black hole is that former travels in 3 dimensional space having no effect on space- time geometry while later travels in opposite direction of flow of time in virtual vertical dimension having large effect on space-time geometry. Hence, if black hole is similar to photon and if photon as quanta of energy having its own temperature, T (T=Energy/ Boltzmann’s constant) never radiates away its energy to the surrounding space, if no external force like gravity is acting on the photon, then black hole also should not have to radiate away its energy to surrounding space because it is quanta of energy (not like any object having matter). Hence, no violation of second law of thermodynamics with no need of radiations from black hole. The only one way in which black hole should radiate its all energy to surrounding space is explosion of black hole itself which will again increase the entropy of the black hole (explosion is irreversible process) not due to increase in energy of the black hole but due to decrease in absolute temperature of the black hole during explosion.

**Conclusion**

This new definition of gravity, clearly abandoned the big bang theory revealing the hidden basic natural force i.e. time. It also clearly shows that moving opposite to the direction of flow of time does not mean to move from present to past as there is nothing like past, present and future. It means simply that time in your frame of reference got slow down as compare to frame of reference where object is at rest. It is impossible to go into past, and to kill your grandfather giving birth to new different feature. Thanks God! Life of grandfather is saved.

**References**

[1] N.C. Garach, Understanding the Relativity

[2] J. R. Brownstein and J. W. Moffat (2006). “Galaxy Rotation Curves Without Non-Baryonic Dark Matter”.

Astrophysical Journal 636: 721. doi:10.1086/498208.

[3] Steven Holzner, Physics for Dummies

[4] Slava G. Turyshev & Viktor T. Toth “The Pioneer Anomaly” in Living Reviews in Relativity (2010)

[5] Stephen Hawking (2001) A Brief History of Time

[6] Stacy E. Palen (2002) Theory and Problems of Astronomy

[7] Slava G. Turyshev & Viktor T. Toth “The Pioneer Anomaly” in Living Reviews in Relativity (2010)

arXiv:1001.3686