Mordred

Bingo. We choose c to follow the 45 degree line. Which makes plotting two Lorentz formulas easier. Time dilation and length contraction. As shown here. http://www.google.ca/url?q=http://www.phas.ubc.ca/~mav/p200/stnotes.pdf&sa=U&ved=0ahUKEwik27S2_fPMAhVY0GMKHb9sBA8QFggiMAU&sig2=3p5OTYqu4FQWehK27ZXdDQ&usg=AFQjCNF41YE6hVXGXB4_-GgwMsnpMn2CGg

Ok so far but what does the 45 degree line represent on the ct vs x graph. second question In terms of y vs x what is the numerical relationship along the 45 degree line. Here is a hint [latex] ct=\frac{v}{c}x[/latex]

Ok show how ct is represented. Also specify what specifically the 45 degree axis represents on a ct vs x graph. I'd like to see if you truly understand why the 45 degrees is chosen in spacetime graphs.

Ah now that's a relationship of a completely different stripe as to what's been presented thus far this thread. However the 45 degree line used in Lorentz is a convenient choice. None of the models presented so far this thread has a ct axis.

Are you aware that angles are considered invariant quantities? "Angles and ratios of distances are invariant under scalings, rotations, translations and reflections. These transformations produce similar shapes, which is the basis of trigonometry" https://en.m.wikipedia.org/wiki/Invariant_(mathematics)

No I want you to show why that plot means 45 degrees is invariant.

Funny I don't see a single math equation in any of your posts. I see a lot of claims but no equations

Fine if the math is so simple to describe as being invariant and you claim to have done that math then post it. It is your claim no one else's. It's time for you to mathematically defend that claim

So let's ask the question "why would you think this animation suggests that direction has a property?" Many of your posts along those lines simply distract from solving the math behind the animation. As far as that goes we've supplied the needed clues as to how to program that animation. In all honesty it merely appears complex.

No you don't you just need a 3d trig function which combines two 2d trig functions.

Then post the math. Quite frankly programming this animation is straight forward.

Steve all you need to do is look for two simultaneous trig operations. Look at how point e moves. If calling two simultaneously operated trig functions count as a new function ( which it doesn't) then sure it's a new function. Every change relates to a change in degrees in two simultaneously operated trig operations. For e one is y to x, the other is z to x. The other clue is the angle between longitude and tangent planes is identical at times. In essence he is applying the same change on the logitude plane and the tangent plane and calling this a new trig function. One example plot f(x,y)=sine(x)+y

Here is a list of properties of trigonometric functions http://www.analyzemath.com/trigonometry/properties.html

I'm a firm believer one must look and study why certain terminology is used and why. These terms aren't arbitrary. It may seem insignificant but proper terminology should always be applied as more often than not the terminology provides clues into key relations. In particular within the definition. If you can show a mathematical property that can be applied to direction following the mathematic or coordinate definition or even the physics definition. Then you might be on to something. However simply trying to apply a terminology without a proper correlation is pointless. The model by Han Milton is extremely simplistic. Anyone can see that, it does nothing to suggest direction is a property. At best Hans animation simply shows the properties of trigonometric functions.

The above doesn't change the fact that distance or direction are both relationships. Not properties by definition. Even in coordinate systems and mathematics not all relations count as properties. For example there are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive property. In terms of shapes example properties are for example The interior angles of a triangle always add up to 180° The exterior angles of a triangle always add up to 360°

There is a difference between polarization and direction. Just because one can predict which direction an object will go doesn't mean that direction is a property. Lets put it another way, just because an object or particle moves a certain direction in relation to an influence doesn't mean the direction itself is a property. A good example being a pool ball. We can easily predict which angle and direction the ball will travel upon being hit or hitting another object. However the direction travel of the ball requires other influences. An intrinsic property doesn't require other influence. Ie intrinsic angular momentum,charge, rest mass etc. ( though mass is debatable as its due to field interaction) it's accepted as a property as all electrons have the same rest mass. In any particle species all members have the same intrinsic properties. In simplistic terms a property is something we can use to classify and identify with all members of a species. Lets look at those pool balls again. List the properties that every pool ball shares in common.

I believe the definition of property has already been given this thread. physical property - any property used to characterize matter and energy and their interactions property - a basic or essential attribute shared by all members of a class; "a study of the physical properties of atomic particles" Direction doesn't qualify as a property. A coordinate system isn't physical, it's a tool used to describe the physical. ( you can arbitrarily use any coordinate system to describe any interaction, field etc )

Think of it this way inertia the the tendency of a body at rest to remain at rest or of a body in motion to stay in motion in a straight line unless acted on by an outside force. So when you stated This statement is incorrect. As a body in motion (inertia) will stay in motion in a straight line until acted upon by a force. Any change in direction or momentum (inertia) is a change in acceleration.

In physics, mass is a property of a physical body. It is generally a measure of an object's resistance to change its state of motion when a force is applied. https://en.m.wikipedia.org/wiki/Mass Inertia The tendency of a body to resist acceleration.

You need to apply the same trig function to two axis. Y to x and z to x. Which I think you've already applied. Lol this reminds me of the problem set I had learning 3d graphics back in the trash 486 days. I asked myself how do you program a 2d screen to have a third dimension. The trig functions bogged down that poor PC lol. Granted I was recalculating each pixel along a line.

Lol there is a significants at pi/4 that does make doing trig relations easier to understand. However it's well known lol.

Roflmao

Not that I can see from the rotation plot on each quadrant. All points on the rotations are easily definable via standard trig. The graphic representation merely plots an identical set of relation change between axis.

Nothing not in the manner the OP thinks it does. Quite frankly what's shown in the animation is basic trig.

Plot movement of e, then plot each planes relation to e. However here is the thing as e moves two planes are getting another rotation. The plane that e follows undergoes Two rotations, (your reference plane) this is the plane that e dissects. however the other two planes which follows the coordinate change in e under go a rotation as e moves. (Which is the degree change) Lol it looks fancy but really it's not. The solution is surprisingly easy. Referring to the graphic Steve wanted to reverse engineer. Programming that is surprisingly easy. Here's a hint because of how easy a math problem it is I don't want to give away the solution. If you remove the reference plane. All quadrants of the x,y,z graph undergo the identical movement.