Friday, October 21, 2016

General Relativity - Einstein Again - Freaky Fzx Friday

Galileo and Newton and all scientists until Einstein considered space and time to be separate and unaffected by the observer.

In 1905 Albert Einstein explained how it was possible that light would be measured the same for all observers no matter the speed of the light source.  It was a triumph of perspective - the facts were all there but took an Einstein to put it all together.


Special Relativity is a collection of facts about how things act when traveling near the speed of light.  It is "Special" because it only deals with objects traveling at a constant velocity.  Special Relativity introduces "SPACETIME"  to our vocabulary - the three dimensions of space and the dimension of time are all related to each other and measurements of spacetime can vary depending on perspective.

It's SPECIAL because it is limited to constant velocity

Now united as one, space and time affect each other

We live in 3 spacial dimensions and one time dimensionj

"At rest" = ANY constant velocity
If you  can't tell the difference by experiment, there is no difference

No longer constants - now dependent upon velocity 
but only from an external perspective
everything looks normal from inside

It took Einstein another decade to figure out how to extend his Special Theory of Relativity to objects that are doing more than just moving at a constant velocity.  This is called his General Theory of Relativity.


If there is no internal experiment that can be done to differentiate among a high constant velocity, a low constant velocity, or "rest" - those states must be equivalent.

In the same way, if there is no internal experiment that can be done to differentiate among a gravitational field and acceleration, those states must be equivalent.  But first back to Newton and his Law of Universal Gravitation.


Let's compare you in a rocket (far from earth) accelerating "up" at 9.8 m/s/s and you in a rocket-shaped room on the surface of earth in a gravitational field of 9.8 N/kg.


If you can't tell the difference between the two with an internal experiment, they must be the same.


One crazy conclusion is that acceleration of an object and the effect of a gravitational field are equivalent.  Let's do another experiment using a laser or a beam of light in an accelerating rocket.


Fire that laser under a massive acceleration and both internally and externally you would see a curved beam.  The floor is moving toward the point of origin of the beam of light.


Remember that equivalence principle - acceleration and g-field are the same so everything that would happen under a huge acceleration...



...would happen in a huge gravitational field.  But if mass attracting mass is what makes gravitational force we have another problem since light has not mass and shouldn't be affected by a gravitational field.



Here's where Einstein's twisted mind comes in again.  If gravity attracts light and bends it but light has no mass, how does it do that?


That pesky spacetime again must be affected not only by relative velocities but by large concentrations of mass and gravitational fields and accelerations.





Mass bends time.  An atomic clock in orbit around earth runs faster than the same one on earth.  Even more slowly at the surface of our sun.  And even more slowly near a black hole.


Ridiculous.  Even more ridiculous is that light is bent when near a big mass like our sun.  It was during a solar eclipse in 1919 that scientists took pictures of the stars around the sun and found a star that should not have been visible.  The light had been bent by the gravitational field near the surface of the sun - the first experimental verification of Einstein's General Theory of Relativity.



BUT - Einstein again - the  light isn't the thing that is bent.  Spacetime is bent and light follows a straight line.


And remember that gravity- acceleration equivalence principle again - the same would happen under acceleration - Acceleration bends spacetime too so that twin paradox isn't a paradox, it just depends on the bending of spacetime under acceleration (gravity field).




That "twin paradox" from last time depends on the acceleration/gravity field effects of General Relativity.

Einstein's twisted mind again.  This time with more math.



Thursday, October 20, 2016

Friction Terms

Here are the friction terms we should use with explanations below.

Types of Friction:

  • Surface Friction - a force parallel to the surfaces in contact that resists sliding
    • Sliding Surface Friction (Kinetic Surface Friction) - Surface friction for two surfaces moving - sliding - past each other.
    • Static Surface Friction - Surface friction for two surfaces at rest with respect to each other - no  sliding.
  • Rolling Friction  - A resistive force on a rolling object because of tire deformation.
  • Fluid Friction - A resistive force on an object moving through a liquid or a gas.
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Sliding Surface Friction

Surfaces sliding past each other

Rear wheels sliding

Static Surface Friction - 

As long as the tires don't slide
a car stays in static friction in normal travel
even though it's moving.

Static - no sliding

Both types of surface friction are dependent upon the NORMAL FORCE between the surfaces and the SURFACES in contact.  Here is the equation - it is a good approximation of reality for smooth and dry and solid  surfaces.


Two additional links on surface friction
          HyperPhysics on friction
          More HyperPhysics on friction

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Rolling Friction - 


Tire base deformed leading to rolling resistance


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Fluid Friction - 





Friday, October 7, 2016

Relative Simultaneity and Aging - Freaky Fzx Friday

Einstein's 1st postulate - his starting point - for Special Theory - is that the speed of light is measured the same no matter the speed of the source or observer.  That was based on the Michelson-Morley experiment from 1887.

Einstein's Special Theory of Relativity is so named because it only deals with the special case of objects moving at a constant speed in a straight line.


This point of view - or Frame of Reference - is called an "inertial frame of reference"


So clocks run slow and mass increases and length contracts but only from the external perspective.

Internally everything looks normal and is measured to be normal and IS normal.  That's Einstein's 2nd postulate.

Simultaneous events in one frame of reference might not be simultaneous in another.  Both are correct.


And our final piece of Special Relativity is the Twin Paradox.  It's called a paradox if you are only looking at it from the Special Relativity perspective.


Next time - General Relativity - The real reason that the traveling twin ages more slowly.