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---------------------- 2271 - How Can Space and Time be Related?.
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- How can space and time be related? They are so different. Space is volume, 3 dimensional volume. Move left, right, forward, backward, up and down and that box of volume is called space.
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- It is the stuff that matter occupies. Remove all the matter and space is what is left. Usually our senses do not experience space, except for the lengths and distances. One thing occupies a space another thing is separated in space occupying a different space. The separation we see as distance. It is 3 dimensional as well.
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- Time on the other hand is one dimensional. How can it be related to space? Time is how we separate events. One event happens after another event. There is a cause then there is an effect that follows the cause. The sequence of events only moves in one direction. It is one dimensional. How can these two things be related?
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- One way they are related is the way we describe motion. Movement through space can be defined as distance only with respect to a reference. Motion is defined as movement through space per unit time.
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- Motion is separation in space divided by separation in time. We call this ratio of the two velocity. When velocity is zero we are at the reference point for space and time. When the ratio of the two is positive we have relative motion with respect to the reference.
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- As long as the relative motion is constant and unchanging there are no external forces involved. Constant motion is a natural state the same as at rest is a natural state. The difference only depends on how you set the reference. Whether at rest at the reference, or in constant motion at a constant velocity in a straight line, then motion is in its natural state and no forces are involved.
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- However, if the velocity speeds up or slows down, or changes direction, then external forces are involved. Even if the speed of motion is constant, if it changes direction from a straight line than an external force is involved. We define either a change in motion or a change in direction as a form of acceleration. Acceleration is the rate of change of the rate of change of space with respect to time.
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- One of the inherent problems with ratios is that they tend to have limits. Numerators divided by denominators tend to produce limits when either approach very large numbers or very small numbers.
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- In the case of velocity, space divided by time, there is a natural limit of 670 million miles per hour. This is nature’s speed limit. No object can pass through space faster than 670 million miles per hour.
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- What makes this natural law especially difficult is that it always applies regardless of relative motion between objects. Objects everywhere regardless of their motion must see the same limit. The laws of physics is the same for all observers everywhere.
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- In order for law to always happen then space and time must change in order to keep the ratio constant for all observers. It also means that when two observers are separated in space there will always be that same limit in the speed of communications between them.
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- Everything you can see or experience has already happened some time ago. Even something you see one foot away, your hand writing on this paper, happened one nanosecond before your eyes could see it.
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- If you look at the clock across the room, you are seeing it 15 nanoseconds after it clicked its second hand. If the event happened on the other side of the Grand Canyon it really occurred 10,000 nanoseconds ago. The first ray of sunlight you see is already 8 minutes old. The stars visible to the naked eye are like they were 10,000 years ago. That starlight is already 10,000 years old.
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- Everything we see or experience is history. There is no way to experience different events as being simultaneous. If events are separated in space they must also be separated in time. Something that appears undecided to you has already happened. And, you will simply have to wait your turn to experience it. In that way reality is what we experience and everyone experiences it differently.
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- In this way time and space are relative quantities and not absolute quantities. The fabric of spacetime together are stretching out in an expanding Universe. Clocks moving through this fabric in different ways tick time at different rates because different amounts of the motion through time transfers into motion through space. At the maximum motion through space time stops. At the maximum motion through time space disappears.
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- Space and time are not absolute quantities. They very with motion through spacetime. Space and time individually adjust themselves in a compensating manner in order to keep the speed of communications between observers the constant 670 million miles per hour regardless of the relative speeds of the observers themselves.
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- The maximum speed through space is reached when all the light speed motion through time is fully diverted into light speed motion through space. Moving at light speed through space leaves no motion for traveling through time. It is only spacetime together that is absolute.
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- It is only against absolute spacetime that objects can be said to be accelerating. Spacetime is the absolute reference for motion. A constant trajectory through spacetime in a straight line is NOT accelerating. Constant motion in a straight line feels no resistance. Photons feel no resistance because they always move at a constant velocity in a straight line in spacetime. Photons feel no acceleration.
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- We can feel acceleration. It provides a force on us. On the surface of the Earth the acceleration we feel is 9.8 meters per second per second. ( 32 feet per second per second).
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- There are two different ways used to model this force that we feel. Either the mass of the Earth is pulling on the mass of your body with a force, called gravity. Or, your body is sliding down the slope of curved spacetime caused by the mass of the Earth creating a curvature in spacetime. The surface of Earth is stopping you from sliding down the slope to the center of the Earth. That is what you feel.
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- It is the same way the Earth is circling the Sun. The Sun’s mass creates a curvature in spacetime and the Earth in constant velocity follows a straight line in spacetime as it orbits the Sun. We do not feel it because we are traveling at a constant 66,500 miles per hour.
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- Actually Earth’s orbit is elliptical and not a perfect circle. Being elliptical , as we are slightly closer to the Sun our speed in orbit increases and as we are slightly farther away from the Sun our speed slows down. 66,500 miles per hour is an average. We will use a circle because the math is simpler.
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- Although our speed in orbit is a constant, our velocity is not because we are constantly changing directions in geometric space. We are orbiting in a circle around the Sun. We are constantly accelerating toward the center of the circle. We model this as the force of gravity pulling us toward the center with a force measurement of:
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-------------------- 35,000,000,000,000,000,000,000,000 Newtons.
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--------------------- ( 35*10^21 kilogram*meters / second^2).
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- The force of gravity is proportional to the product of the masses and inversely proportional to the square of the distance between them.
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----------------- The radius of Earth’s orbit is 93 million miles.
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---------------- The circumference of Earth’s orbit is 584 million miles, 2* pi* r
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---------------- The mass of the Earth is 5.97 * 10^24 kilograms.
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----------------- The mass of the Sun is 1.99*10^30 kilograms.
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----------------- The Gravitational Constant of Proportionality is 6.67*10^-11 meters^3/ (kilogram * seconds^2)
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---------------- F = G * m* M / r^2
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--------------- F = 35 * 10^21 Newtons.
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- The force of gravity is exactly balanced by the centripetal force of the Earth trying to pull away and travel in a straight geometric line. The centripetal force is:
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-------------------------- - 35,000,000,000,000,000,000,000 Newtons.
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- The Centripetal Force is the mass of the Earth times the acceleration of the change of direction of velocity towards the center of the circle.
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------------------------ F = m * a
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- The acceleration is the tangential velocity squared divided by the radius of the circle of orbit.
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-------------------------a = v^2 / r
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------------------------ F = m * v^2 / r
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----------------------- The mass of the Earth is 5.97 * 10^24 kilograms.
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---------------------- The velocity is 66,500 miles per hour.
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----------------------- The radius of Earth’s orbit is 93 million miles.
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----------------------- F = 35 * 10^21 Newtons.
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- The two forces offset each other and we feel no net effect.
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- These calculations use the models developed by Isaac Newton and they work well when the rate of space / time is far from its limits. As motion approaches the speed of communications between separations in space then the more complex models developed by Albert Einstein are needed.
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- At faster speeds and greater accelerations of gravity then the interrelationship between space and time become noticeable. Their ratio must not exceed the speed of communications between objects regardless of the relative speeds of the objects themselves. As strange as this may seem? The reality that we observe may have little to do with the reality that is out there.
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- February 13, 2019 1241
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-------------------------- Thursday, February 14, 2019 --------------------------
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