- 2054
- Relativity
starts with a very simple concept. It
starts with all motion being relative.
Space and Time require a reference frame in order to be measured. Next, the laws of physics are always the same
regardless of where you are or what is in motion. 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.
E = mc^2
-
-
-
---------------------------------- 2054 -- Relativity Explained.
-
- Relativity
starts with a very simple concept. It
starts with all motion being relative.
Space and Time require a reference frame in order to be measured. There is no dimension in space or interval in
time without it being in reference to something else. All observers see things from different
space-time perspectives.
-
- Next, 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. Light is always traveling at a constant speed
for everyone, 186,355 miles per second, or, 299,792,458 meters per second,
exactly.
-
- 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. 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.
-
- Distance
actual =
Distance measured - velocity * time
-
- 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.
-
- 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.
-
-------------------------- Distance B
= Distance A
-
velocity * Time B
-
-------------------------- Time Observer B = Time
Observer A
-
- 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:
--------------
(1/(1-v^2/c^2)^2 = Time^2 - Distance^2/c^2
- 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.
-
----------------
Space - Time Interval = constant
- 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.
-
--------Space-Time interval^2 = Time^2 -
(Distance/c)^2
-
- 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.
-
--------------- Time B^2 - (Distance B/c)^2 = Time A^2 - (Distance A/c)^2
-
- In order to
make the two intervals the same regardless of their motion we must add the
factor, 1/(1-v^2/c^2)^.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:
-
----------------------- Distance B = Distance A * (1-v^2/c^2)^.5
-
- If the
velocity is 87% the speed of light, then the distance is shortened to 50% for
Observer B.
-
----- (1-v^2/c^2)^.5 =
(1-.87^2)^.5 = (1-.76)^.5
= (.24)^.5 = .50
-
- 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:
-
------------------------ Time B
= Time
A / (1-v^2/c^2)^.5
-
------------------------ Time B
= Time
A / .50nn = 1/.5 = 2 seconds
-
- mNow 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.
-
- Time is
related to Energy.
-
- Space is
related to Momentum
-
- The constant
Interval of Time = Time^2 - Distance^2/ c^2
-
- The constant
Interval of Energy = Energy^2 - Momentum^2/c^2
-
- 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.
-
- 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:
-
----------------------
Energy^2 - mass^2 * velocity^2 / c^2 m = mass^2 * c^4
-
---------------------
If an object is “at rest”, velocity = 0
-
--------------------
Energy^2 = mass^2 * c^4
-
--------------------
Energy = mass * c^2
-
----------------------- E = mc^2
-
- If the object
is moving:
-
----------------------
Energy = mass * c^2 + mass * velocity^2/2
-
- The second
term, ½ mv^2 is the formula for Kinetic Energy.
-
- Total Energy
is equal to Rest Energy + Kinetic Energy.
-
- If an object
is at rest it still has energy. A
profound conclusion.
-
---------------------------- E = mc^2
-
- In comparing
objects in motion, Newton said:
-
Energy = ½ m*v^2
-
Einstein said:
Energy = m*c^2/(1-v^2/c^2)^.5 and Momentum
= m*v /(1-v^2/c^2)^.5
-
- 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.
-
- 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.
-
- 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.
-
- 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.
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.
-
- Length and
distance are just another word for measurements of space. Distance measured by an observer in motion = m distance - velocity * time
-
- As an
observer’s motion approaches the speed of light this correction factor is
needed to shorten distances and slow time.
-
---------
Distance = 1/(1-v^2/c^2)^.5 * (distance - velocity* time)
-
---------
Time = 1/(1-v^2/c^2)^.5 * ( Time - velocity * distance) / c^2
-
- 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. Of course, logic is in the
mind of the beholder. I hope me
explanations make a little bit of sense.
Let me know?
-
-------------------------------------
----
Comments appreciated and Pass it on to whomever is interested. ----
---
Some reviews are at:
--------------
http://jdetrick.blogspot.com -----
--
email feedback, corrections, request for copies or Index of all reviews
------------------------- Tuesday, April 10, 2018
--------------------------------
No comments:
Post a Comment