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--------------------------- 2417 - RELATIVITY - best I can explain it.
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- All observers see things from different space-time perspectives. Light is a physical symmetry for the entire universe.
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- The laws of physics are always the same regardless of where you are or what is in motion. All states of uniform motion are equivalent. Light always appears the same to all observers regardless of their motion.
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- Light is always traveling at a constant speed for everyone, 186,355 miles per second, or, 299,792,458 meters per second, exactly.
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- Any two events are separated in time and space by definition. In order to measure the time we need to synchronize our watches. We start at point A and Watches A and B are synchronized so they measure exactly the same time. We travel a distance to point B and measure how much time it takes.
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- If we know our velocity it is an easy calculation, Distance = velocity * time. Now let’s say we are at point B and we want to synchronize our watch with the Watch at point A. Maybe we use a flash of light, or a telegraph signal to set our watch at point B. The watches can not easily be synchronized at a distance because there is a delay in the time it takes the light or the signal to reach the observer B at that distance.
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---------------------- Distance actual = Distance measured - velocity * time
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- Where velocity is the velocity of the signal, which could be the speed of light. The separate events can not occur simultaneously because the information that connects them only travels at the speed of light.
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- Newton made “time absolute“. All observers, no matter how they move through space, must conclude that the time interval between any two events is the same.
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-------------------------- Distance B = Distance A - velocity * Time B
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-------------------------- Time Observer B = Time Observer A
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- Einstein proved this concept of “absolute time” to be WRONG. Newton’s formulas only work for low velocities. As velocities approach the speed of light the new relativity formulas apply:
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--------------------------- (1/(1-v^2/c^2)^2 = Time^2 - Distance^2/c^2
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- Where v is velocity and c is the speed of light.
- Any two events are separated in time and space, but, the interval between the two events must remain the same regardless of which observer makes the measurements. In order for that to happen time and space need to be relative.
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---------------- Space-Time Interval = constant
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- Space-Time is a vector that has both magnitude and direction. Any vector is a magnitude at some angle. You can always construct a right triangle and solve the magnitude of the vector as the hypotenuse = the square root of the sum of the squares of the other two sides of the triangle. The Pythagorean Theorem.
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--------------------Space-Time interval^2 = Time^2 - (Distance/c)^2
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- The two events in space-time are connected by a light signal. Each observer, all observers , will conclude that the speed of light is the same, no matter what velocity or direction they are moving. So, the above formula can be written twice, once for observer A and the other for observer B.
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-------------- Time B^2 - (Distance B/c)^2 = Time A^2 - (Distance A/c)^2
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- In order to make the two intervals the same regardless of their motion we must add the factor, 1/(1-v^2/c^2)^0.5 This Space-Time Interval factor guarantees that a light flash spreads out spherically into space the same way for all observers.
- At low speeds relativity is an unobservable correction for moving objects. But, at higher speeds distances are shortened by the factor:
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------------------- Distance B = Distance A * (1-v^2/c^2)^0.5
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- If the velocity is 87% the speed of light, then the distance is shortened to 50% for Observer B.
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----- (1-v^2/c^2)^0.5 = (1-.87^2)^0.5 = (1-.76)^.5 = (.24)^0.5 = .50
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- If the velocity is 87% the speed of light and the time is measured at one second, then the time is slowed down and the time interval for Observer B becomes 2 seconds:
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------------ Time B = Time A / (1-v^2/c^2)^0.5
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------------ Time B = Time A / .50nn = 1/.5 = 2 seconds
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- Now that space and time are changing with the velocity of motion Einstein concluded that Force, Momentum, and Energy equations could also not remain the same under the 1/(1-v^2/c^2)^.5 transformations. If this symmetry between space and time exists then this same symmetry between energy and momentum must exist.
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----------------------------- Time is related to Energy.
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----------------------------- Space is related to Momentum
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----------------------------- The constant Interval of Time = Time^2 - Distance^2/ c^2
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------------------------- The constant Interval of Energy = Energy^2 - Momentum^2/c^2
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- For the speed of light to remain constant and the Energy Interval to remain constant then the Energy measured by Observer A must be different than the Energy measured by Observer B.
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- Einstein guessed that this formula must also be equal to the Inertial Mass, but he had to square it in order to get the units to cancel. And, Momentum = mass * velocity:
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----------------------------- Energy^2 - mass^2 * velocity^2 / c^2 = mass^2 * c^4
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----------------------------- If an object is “at rest”, velocity = 0
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----------------------------- Energy^2 = mass^2 * c^4
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----------------------------- Energy = mass * c^2
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----------------------------- E = mc^2
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------------------------------------------- If the object is moving:
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----------------------------- Energy = mass * c^2 + mass * velocity^2/2
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----------------------------- The second term, ½ mv^2 is the formula for Kinetic Energy.
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----------------------------- Total Energy is equal to Rest Energy + Kinetic Energy.
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----------------------------- If an object is at rest it still has energy. A profound conclusion.
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----------------------------- E = mc^2
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- In comparing objects in motion, Newton said:
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----------------------------- Energy = ½ m*v^2
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----------------------------- Einstein said:-
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--------------- Energy = m*c^2/(1-v^2/c^2)^.5 and Momentum = m*v /(1-v^2/c^2)^.5
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- As velocity approaches the speed of light, v approaches c, then Momentum and Energy become infinite. That is why nothing can exceed the speed of light. It would take infinite energy to accelerate to that speed and the particle would have infinite momentum.
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- If an object is massless the formula becomes indeterminate, 0/0. However, this indeterminate allows a massless particle to have finite energy and momentum. Massless photons of light have no Inertial Mass yet photons can transmit energy and momentum through space.
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- Photons travel forever at the speed of light. They can not travel slower or be at rest because their energy would be zero. If photons move it is at one speed only, 186,355 miles per second.
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- Einstein’s concepts are hard to explain, but it is just the way it has to be to make the equations work out. Start with a simple assumption, the speed of light is constant. Then, the rest is in the math.
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- Every experiment physicists have tried, so far, confirms that the math is correct. Space does truly shrink, and time does truly slow down as velocity approaches the speed of light. The laws of physics have got to remain the same for all observers regardless of their relative motion.
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- Length and distance are just another word for measurements of space. Distance measured by an observer in motion = distance - velocity * time
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- As an observer’s motion approaches the speed of light this correction factor is needed to shorten distances and slow time.
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------------------ Distance = 1/(1-v^2/c^2)^.5 * (distance - velocity* time)
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------------------ Time = 1/(1-v^2/c^2)^.5 * ( Time - velocity * distance /c^2
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- Light is a physical symmetry for the entire Universe. Albert Einstein came up with these concepts when he was 26 years old. His discoveries were never experimental, he used “thought experiments“. He exercised all the concepts in his mind and took them to their logical conclusions.
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- Of course, logic is in the mind of the beholder. I hope me explanations make a little bit of sense. Let me know?
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- July 13, 2019 648
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--------------------- Saturday, July 13, 2019--------------------
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