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Relativity And Simple Algebra

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#868 sluggo

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Posted 08 July 2019 - 09:38 AM

"If Bob drove 60 miles at 60 mph to see Alice, he would see her in 60 min. If he asked her to leave at the same time and drive to meet him, he would see her in 30 min. No one exceeded the speed limit, they only drove half the distance simultaneously.]"

 

But the relative velocity would be 120 mph. Alice's car is going 60 mph towards Bob. Bob's car is going 60 mph towards Alice. No one is exceeding the speed limit but their relative velocity is 120 mph. The gap between them is also closing at 120 mph which a person on the side of the road witnesses. The closing speed equals the relative velocity except for an insignificant relativistic effect. But with higher relativistic effect, the closing speed gets up to two times the relative velocity. Bob and Alice could  see their relative velocity is also 120mph with radar guns. I just don't see how two cars headed towards each other wouldn't crash at twice the speed as one would being parked and the other hitting him at 60mph. That's how head on collisions work. If what you're saying is true then we live in 2 different physical universes.

 

 

Agree with gap closing at 120. Alice moves 30 mi in 30 min, v=60. Bob moves 30 mi in 30 min, v=60.

Note, they move simultaneously 

We have accounted for all objects in motion. Where is the thing moving at 120?



#869 sluggo

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Posted 08 July 2019 - 09:56 AM

Also true is the fact that sound is not effected by the motion of the person hearing it. 

 

Doppler shift results from relative motion of source and detector.

Most people have heard the variation from sirens.



#870 ralfcis

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Posted 08 July 2019 - 10:11 AM

Where is the thing moving at 120?

 

The thing is called relative velocity. They are each moving at 60 mph relative to the road but they are moving at 120mph relative to each other. The closing speed, as viewed by someone watching them from the side of the road, is not a relative velocity. It does not depend on how close he is to them or even if he's directly in line with them. But relative velocity of each to him does depend on how far he is from the road because relative velocity is a vector. If he was watching two satellites closing at 120mph, their relative velocity to each other would be 120 mph but to him it would be near zero. No? None of this sounds familiar?


Edited by ralfcis, 08 July 2019 - 10:38 AM.


#871 sluggo

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Posted 09 July 2019 - 10:43 AM

Ralf;

 

But with higher relativistic effect, the closing speed gets up to two times the relative velocity.

 



[Composition of velocities does not agree.

B velocity v, as measured by A, v = (b-a)/(1-ab), a = .9 and b=-.9.

v= -1.8/1.81 = .99.]
 



#872 sluggo

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Posted 09 July 2019 - 10:46 AM

Ralf;

The bus is mostly empty now. A ride to nowhere.
This is where I get off.



#873 ralfcis

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Posted 09 July 2019 - 11:18 AM

You really are illiterate. I said closing speed can be 2c  not relative velocity which must always be less than c according to the velocity combo law. Where do you get the balls to think you can discuss relativity when you don't even know what relative velocity is? Please stay off the bus this time until you learn some basic terms at least. I wouldn't be surprised if no one here knows what velocity is let alone relative velocity because they let your total ignorance pass without a word.



#874 ralfcis

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Posted 09 July 2019 - 11:34 AM

Since you're too lazy  to google questions here's a link for you

 

https://www.quora.co...locity-addition

 

I know you have severe reading disabilities but you're going to have to try to join the letters into words, words into sentences and use that place holder between your ears to try to make sense of the sentences.



#875 ralfcis

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Posted 09 July 2019 - 09:18 PM

I'm hoping everyone got off the bus with Sluggo because I'm going to go way off road. I'm going to try to derive new math for velocity addition based on Yv + Yu = ?. It should be a more linear way to add velocities than Einstein's equation and should require no hidden tricks to make things look like they apparently work. The math will look nothing like Einy's math and be based on none of his assumptions so relativists will have no hope of understanding it. They're pretty busy with trying to understand what relative velocity is so they may not have time to grasp the new math. Don't know how long it will take or when I'll start or if it'll be ultimately successful so this may be a rabbit hole you might want to avoid as I flail around.



#876 ralfcis

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Posted Yesterday, 10:06 AM

Ok equations and their derivations are coming. Here's what I have so far but it's not formally derived:

 

The first equation, as you may remember, is the relative velocity to c.

 

DSR = Yv(1-v/c) if v is negative.

 

example v= -.6c (Alice going back to Bob)

Yv = 1.25 (I've added the subscript because when I start adding velocities you need to know which Y belongs with which velocity)

DSR = 1.25 (1.6) =2

 

What's interesting in this equation is the sign of v controls the inverse of DSR.

 

if v=.6c (Alice going away from Bob)

DSR = 1.25 (.4) = 1/2 which is the inverse of the original DSR. (Doppler Shift ratio).

 

These tricks come in handy when you want to reduce complex expressions with squares, ratios and square roots into expressions of simple addition.

 

From this I can derive an intermediate equation on my way to linearizing the velocity combo law:

 

Yvv=2Yh2v

 

An example of this is if you want to express .6c relative to a stationary earth as two ships leaving earth in opposite directions at 1/3c which is the half speed vh of v=.6c. Notice I try to make my math accessible unlike 006 which tries to obfuscate what he's doing like frauds tend to do.

 

So putting in these numbers we get

1.25(.6) = 2(1.06)2 /3 and it checks out if any of you know how to use a slide rule. (sarcasm)

 

So the above formula shows how to add 2 half velocities, the next shows how to add any velocities:

 

Yww = (v+u)YvYu where Yw=YvY(1+vu/c)

 

For example v=.6c and u=.8c. What is the combination w of these two velocities?

 

v=.6, Yv=1.25=5/4

u=.8. Yu=5/3

YvY= 25/12

YvY(1+vu/c) = 37/12

w=((1.4)25/12)/(37/12)=.9459

 

This is some extremely powerful math. Let's do another example.

v=1/3c and u = 1/2c

Yv= 1.06066 and Yu = 1.1547

YvY= 1.22474

YvYu (1+vu/c) = 1.428868

w=((.833)1.225)/1.428 = .7142c

 

Let's check that against the old formula:

w=c(v+u)/(c+vu) = .833/1.167=.7142c

 

You might look at this and say, hey man, the old equation looks simpler. Figuring out w is not the goal, Yww is the goal because velocity expressed in terms of Yv is not subject to a limit, velocities expressed as Yv can be linearly added according to the formula above and them converted into Einy's expressions of v limited by c. This new math will have powerful implications later.

 

Yww =YuYvv +YuYvu where Yw=YuYv(1+vu/c) .

 

I'm not really interested in any critiques from math illiterates if you're thinking on commenting.


Edited by ralfcis, Yesterday, 10:08 AM.


#877 ralfcis

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Posted Yesterday, 11:48 AM

I just noticed DSR is independent of how you depict relative velocity. For example, DSR is the same between two opposite velocities at 1/3 c as it is for .6c relative to a stationary reference frame. This is not true for Y in Einy's theory. So converting the above equations using DSR instead of Y would make them truly based on relative velocity independent of a reference frame. DSR is based on light signals which are independent of perspective lines of simultaneity. Causal time is also based on independence from a reference frame. I'm going to explore where this leads next. Does anyone need more detailed clarification?


Edited by ralfcis, Yesterday, 11:48 AM.


#878 ralfcis

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Posted Yesterday, 10:20 PM

Ok I've been skipping ahead to the answers without doing the formal math derivation because I just don't have the time. It's not like anyone here is going to notice. Plus when you know the answer it's easier to work backwards from that. So the answer is if you want the sum of two velocities you use these two formulas:

 

1/DSRw = DSRv * DSRwhere DSRw2=(c-w)/(c+w) and the sign for w is negative for separation (previously it was positive for separation so some of my previous work needs fixing).

 

So let's do an example

 

Alice is leaving earth at .6c and Bob is leaving earth in the opposite direction at .8c. What is their relative velocity to each other?

 

We know from the 2nd formula that DSRv = 1/2 and DSRu = 1/3

 

so plugging that into the 1st formula we get DSRw =6

 

Now we want to solve for w in the 2nd formula and we get w = -35/37c = -.9459c

 

This is the same result as the old formula got for the relativistic combination of .6c and .8c but in a much simpler way arithmetically. No more Y, no more time dilation or relativity of simultaneity or lines of perspective simultaneity (aka length contraction) need be calculated. Since light lines define the DSR and can be used to sync clocks, Einy's clock sync method also ends up in the trash. There's also a new clock start method, using the causal line of simultaneity, for the start of the spacetime path for when the participants do not start co-located. This new velocity combo law, along with the abolition of Einy's spacetime path rules, will make quick work of calculating age difference without the requirement of co-location at the end of the path. Pretty damn neat if I do say so myself even if no one here has a clue of what I'm talking about. Now I just gotta sit here and wait to be discovered.


Edited by ralfcis, Yesterday, 10:41 PM.




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