Relativity And Simple Algebra

[ralfcis]

Polly, I hate to break it to you but no one knows what you're saying and even more, no one wants to find out.

[Moronium]

You saw Post # 100? That is Einstein's velocity addition formula.

 

You are asking me to explain this formula?

 

I can do that but not now. It will take some time and it will involve a fair bit of math.

 

Do you really want to go there?

 

No, I'm saying (asking) this:

 

I see that in you answer you capitalize VELOCITY for emphasis.  But I'm not getting the significance of the distinction between velocity an speed here.

 

 

 

What would the significance be, seeing as how all three objects are aligned in a straight line? What is the big difference between VELOCITY and speed here?  I can see that it would make a difference if one was going north and the other east--perpendicular to each other.  But they're not.  They're going in opposite directions (forming a line).

 

The speed is the velocity.  As I said earlier:

 

But when it's all in one dimension (a straight line), velocity is speed, right?  Although velocity may technically be a vector, it's basically a scalar in those circumstances.  That's different than a guy travelling in a circle.

 

Relative to a given point you can say a guy is going north at 100 mph but nothing changes if you leave out the word "north."  You could substitute east, south, or west, and it would still be the same, i.e, 100 mph relative to that given point.

 

 

What difference does it make, with respect to relative speed, to say that one is going east and the other west?  Does that change their speed?  If so, how? If not, how does capitalizing the word VELOCITY answer my questions?

 

It seems to me that it's a distinction without a difference.

 

In most contexts the words "sufficient" and "enough" are synonyms.  It's true that they are different words, but the meaning is the same, so there's no meaningful difference.

Edited February 20, 2019 by Moronium

[Moronium]

Ok so every velocity on earth is relative to earth. So a jet goes 750 mph relative to earth but if he's closing in on a jet going 740 mph, his closing speed is 10 mph. Relativity would call that relative velocity between the two planes but due to the relativistic velocity combo formula, that relative velocity would be slightly less than 10 mph. At high speed, relative velocity becomes much less than closing velocity which remains Newton's definition of relative velocity. Is that correct now?

 

 

That sounds right, except for this part:  "which remains Newton's definition of relative velocity."  And this part:  ".At high speed, relative velocity becomes much less than closing velocity." It's the other way around.  With SR, relative velocity becomes much LESS than closing speed.

 

Just for the hell of it, I'll ask you if you understand the questions I have just asked Popeye (and the statements I'm making in them).  I'm talking about posts 136 and 154.

 

As I said before, I consider Einstein's formula to be irrelevant mathematical claptrap.   It's "necessary," mathematically, to enforce Einstein's dictate, but it doesn't make sense from any physical perspective.

Edited February 20, 2019 by Moronium

[Moronium]

 Is closing speed used in relativity?

 

Closing speed is used everywhere.  Popeye apparently believes there is a difference between "velocity" and "speed" in the case we're considering.  My contention is that there is no significant difference in that case.

 

He (SR) starts with the closing speed in the formula, then "adjusts" it.  

 

But why is an "adjustment" needed?  If you ask me, it isn't.  

 

If you ask SR, they'll say that it's because it is impossible for anything to exceed the speed of light.  This presupposes the validity of SR's constant light speed postulation, which I reject.

 

I reject it because if you accept it, you end up with claims that are physically impossible.

 

The attempt to somehow distinguish relative velocity from speed (whether "closing speed" or not) does not answer the questions.

Edited February 20, 2019 by Moronium

[ralfcis]

I'll take a crack at it but this is new to me too so I'm just awaiting confirmation I understand it correctly.

 

 "What is the big difference between VELOCITY and speed here? "

 

As I said closing speed is Newtonian relative velocity  while relativistic relative velocity is limited to c by the relativistic velocity combo equation. So the newtonian relative velocity, (which looks like a vector to me), is 1.6c and the relativistic relative velocity is limited by the equation to 40/41 c. So that's a big difference. The newtonian speed magnitude changes due to angle of approach so I don't understand why that isn't a vector velocity. In my example the jets are following in line but at any other angle the speed would change where at head on the closing speed would be 1490 mph.

 

I also don't understand why the relativistic relative velocity is a vector velocity. In the GPS example, the satellites are in free fall around the earth and whether they're approaching or receding from the earth clock the time dilation is the same (but the doppler shift ratio is not). If the orbit of these satellites were several billion miles out, they would not be receding or approaching the earth clock much yet their orbital velocity could be very great. Would the magnitude of that orbital velocity cause time dilation? If so, then relativistic relative velocity would not be a vector but a speed as only its relative magnitude causes time dilation. No?

 

PS. I learned later on that the magnitude of the velocity does not cause time dilation, it requires a head-on direction. The closing speed is a parallel direction, such as across the sky, and when the head-on vectors are summed, they sum to close to zero average velocity relative to the observer's sideways perspective.

Edited February 23, 2019 by ralfcis

[Moronium]

I also don't understand why the relativistic relative velocity is a vector velocity.

 

My point is that isn't doesn't matter if you treat it as a vector or not, at least in the case we're talking about here.  Here, "velocity" just reduces to "speed."  They're the same things.  Don't let the difference in terminology confuse you.

 

Did you read the posts, I asked you about?

Edited February 20, 2019 by Moronium

[Moronium]

You're missing the real point, Ralf, which is the one I outlined in post #160.

 

The real question is--why does the relativistic addition formula exist at all?

 

Saying that velocity is a vector is not really relevant to that question.

[Moronium]

So the newtonian relative velocity, (which looks like a vector to me), is 1.6c and the relativistic relative velocity is limited by the equation to 40/41 c. So that's a big difference. 

 

 

I agree that it's a big difference in the answers you get.  I just mean there's no difference between velocity and speed in this case.

Edited February 20, 2019 by Moronium

[Moronium]

A and B sees their relative velocity as being 1.6c

 

Note that the earth also "sees" their relative speed as 1.6c (prior to calculations), so they all agree, to start with.  But then the "calculations" begin, and then earth observers "sees" (sees is NOT the right word, calculates with a formula is) their relative speed as being .975c.

 

Which is right (true), 1.6c or .975c?

 

Both?

 

Neither?

Edited February 20, 2019 by Moronium

[ralfcis]

1.6c is not the correct answer to your specific question. If the relativistic combo law was not correct, no relativistic effects would be measured. MM would have found an ether to which we can measure a relative velocity, time dilation would not exist in the GPS, muons would not be able to reach earth.

 

 

Edited December 19, 2019 by ralfcis

[Moronium]

I haven't watched the whole presentation yet, but notice that Greene is simply talking about speed, not velocity (which is fine). Then he starts using the symbol v in his math.  But he talking about the same thing, i.e., speed, in both contexts.

 

He also states that the speed of light is constant, as though it were a fact.

 

It's not a "fact," it's an assumption.

 

It's an assumption that, if made, leads to all kinds of claims that are physically impossible.

Edited February 20, 2019 by Moronium

[ralfcis]

I heard you the first 50 times but the more often you repeat it, the farther you get from understanding it not that you ever will. But I will admit the argument Greene gives is very circular in that it's impossible to tell the difference between a hypothesis and a conclusion. Did the combo law come first or did the Lorentz transforms or did time dilation? My algebraic derivation at least has a simple start based purely in algebra without requiring any physical phenomena.

 

PS. As I said, I'll only be using closing speed for light signal propagation between the two participants. It's not required for their relativistic relative velocities.

Edited February 20, 2019 by ralfcis

[Moronium]

I heard you the first 50 times but the more often you repeat it, the farther you get from understanding it not that you ever will.

 

 

What is "it", Ralf?

[Moronium]

I have spent a lot of time in this forum pointing out there are alternative theories of relative motion which DENY that the speed of light is constant.  These theories are perfectly coherent and consistent, both mathematically and conceptually.

 

Those theories pass every experimental test that SR does, and more.

 

What's the difference?  Well, one is this:   With the alternate theories you can throw Greene's math out the window.  It doesn't apply. In the process, these theories eliminate all the seemingly endless "paradoxes" generated by SR.

 

You're free to "believe in" SR if you want.  But anyone who knows anything about science can tell you that it is just based on assumptions, not proven "facts."

Edited February 20, 2019 by Moronium

[ralfcis]

It:

It's an assumption that, if made, leads to all kinds of claims that are physically impossible.

 

I just want to try to understand what the majority of scientists see in relativity. I'd just like to see one explain away all the contradictions I see. I felt I was getting close until I saw how relativity defines time and so I'm very close to giving up on it forever. Maybe one of the other theories will satisfy my objections. I was doing just fine with my own theory until I hit that roadblock of Alice returning to earth at near c where she doesn't age while light takes 3 yrs to cover the distance back. There must be another explanation because that one leads to all kinds of claims that are physically impossible. Time expansion for Bob's frame sounded good and is still mathematically feasible but physically nonsense.

Edited February 20, 2019 by ralfcis

[Moronium]

It:

It's an assumption that, if made, leads to all kinds of claims that are physically impossible.

 

Yeah, it is.  And that can be shown in a great variety of ways.  But here's one:

 

According to SR, B's clock runs slower than A, AND A's clock runs slower than B's.

 

That's physically (and logically) impossible.

 

But help yourself if you want to believe that.

Edited February 20, 2019 by Moronium

[ralfcis]

If you go back to my football throwing example. If Bob yells at Harry as Harry is running toward Bob, the speed of sound is not dependent on Harry's or Bob's velocities but Harry's motion towards the sound is a closing speed which combines with the sound velocity to make a Newtonian relative velocity of 30 mph. 

 

Now if you impose a max velocity of 15 mph on the universe, you still get a closing speed total of 30 mph but now you get a relativistic relative velocity of only 15 mph because of the max relative velocity speed limit. Comprende?