Relativity And Simple Algebra

[Moronium]

I was once asked this question (but not in multiple choice form)  and answered correctly within seconds.  There was no effort involved.  Nothing the least bit complicated about it.

 

The answer is 5. None of the above.  Going the speed of light (choice 4) is the closest to being right, but that would not be fast enough.  Nor would a speed of 10c be fast enough.  Or 50c, or 100c.  That should be almost immediately obvious.  Only a basic analysis of the situation is required.

 

The correct answer is that you would have to travel at an infinite speed (i.e., instantaneously) to average 60 mph over the whole course.  But you have no clue about why that is.

Edited March 14, 2019 by Moronium

[ralfcis]

Now back to some real math.

 

In my last post I stated the closer Alice gets to +c away from Bob (as her velocity choice at the turning point), the closer the permanent age difference gets to 2. Now I've said age difference is determined by the intersection of the half speed line of proper simultaneity from when Bob 8 receives the news of Alice's change of velocity to Alice's new velocity line. The problem all of you who don't know math couldn't see is that as v approaches c, the slope of both lines becomes 1. So they're parallel, they can't intersect unless at infinity. How then can I claim they intersect at the number 2 when v=c? They seem to as you plug higher and higher values of v into the equations but that's not a rigorous proof. What's happening is Y approaches infinity as v approaches c. Two infinities are battling it out for who has the right answer. The units on Alice's c line grow to infinity as the slope of the half speed line approaches 1. This looks like an intersection is possible but you're aiming a bullet at infinity, why does it land at the number 2?

 

Cancelling out infinities from equations is difficult but I've seen a possible clue on how to do it in this instance. I've noticed a pattern between Alice's velocities re-uniting with Bob and the ones where she takes on higher velocities than +.6c away from Bob. The age difference numbers at reunion are 4, 3.4, 2.8, 2.5, 2 for Alice's velocities of -c, -40/41c, -15/17c, -.8c, -.6c. The age differences in the opposite direction at .6c, .8c, 15/17c, 40/41c and c  are 0, .5, .8, 1.4, 2. Same pattern but 2 is subtracted from each number.

 

You'd assume 2 is significant somehow, where does it come from. I don't know and it's not important right now. The important number is 6. If Alice ends up 2 yrs older  than Bob when she chooses +c, this means during the time of relative velocity imbalance, Alice and Bob go from age 4 to Bob ending up at 8 and Alice ending up 10 which is a difference of 6 yrs for her.

 

6 is significant in the equations in the calculation of the slopes of the two intersecting lines. Here are the equations again:

 

( x-3 ) /ct = v   and  x / ( ct - 3 )  = half speed v_h

Correction: my new formulas are ( x-3 ) /t = v/c and  x / ( t - 3 )  = c/v_h

v and v_h are related through the formula:

 

v = 2c²v_h / (c²+v_h²) which is the velocity combo law for half speed velocities.

 

We want to get an answer for t which is the intersection point of the two lines in Bob yrs. We really want the answer in Alice yrs because the units of those grow exponentially as v -> c. So using the  time dilation formula we want t' = t/Y as the answer.

 

So using numerology and witchcraft we cast a spell and arrive at the following equations:

Correction: go to post 478 for updated derivation

 

 

Here's where the equations come from graphically using an example of Alice choosing .8c away from Bob for anyone who wants to follow:

 

https://photos.app.goo.gl/vnkiKWuatoDRfH8J8

Edited December 20, 2019 by ralfcis

[ralfcis]

So I need to prove Yv = 1/(v- v_h)  as v-> c

 

I still haven't come up with an algabraic proof but I can clearly see the trend if I use large numbers for v

 

v = 3280/3281

Y = 40.50617 etc.

v_h = 40/41

 

To simplify the calculation  Y = 1/(1- v_h/v) as v -> c

 

Using numbers 40.506 = 1/ (1- (40/41)/(3280/3281))  =41.506 which is very close and shows how as Y grows the other side of the equation gets closer and closer to it.

 

This indicates that as v->c,  sqrt(1-v²/c² ) = v(v-v_h)  where v = 2v_h/(1+v_h²)

 

That seems like a very powerful equation for getting rid of infinities in relativity. Maybe a real mathematician can prove it algebraically for me.

 

 I just found this equation here satisfies all velocities, not just as v->c, and it's a very similar equation:

 

Y+1 = 1/(1- v_h/v)

Edited March 14, 2019 by ralfcis

[Amplituhedron]

ralfcis?

 

You are a total idiot, just like Moron.

 

But do carry on. It's amusing. 

[ralfcis]

Ok I finished my algebraic proof and it's a doozy. My original equation relating v and v_h  was corrected to

 

 v = 2 c² v_h/ (c² + v_h²).  This forced me to correct the rest of the math here

 

Y = c / sqrt(c²-v²) = c / sqrt (c² - 4c⁴v_h² / (c²+v_h²)² )

 

= c (c²+v_h²) / sqrt (c⁶ + 2c⁴v_h² + c²v_h⁴ - 4c⁴v_h²)

 

= (c² + v_h²) /sqrt ((c² - v_h²)²)

 

So Y = (c² + v_h²) / (c² - v_h²).

 

Yv = ((c² + v_h²) / (c² - v_h²))( 2c²v_h / (c²+v_h²))

 

So Yv = 2c²v_h / (c² - v_h²)

 

Ok these are 2 important equations for Y and Yv.

 

I will use them to derive this 3rd important equation

 

Y+1 = 1/(1- v_h/v)

 

After much agony and days of computational errors I was able to derive an alternate form for the equation 

v = 2 c² v_h/ (c² + v_h²)

 

to  v/(c-v) =2cv_h / (c-v_h)² 

 

This allows 2-way conversion between v and its half speed value v_h.

Edited March 19, 2019 by ralfcis

[Vmedvil2]

In any case, I wanted to add in did you know you could put the relativistic vectors in a very simple Killing Vector group in 4 dimensional algebra (Δx',Δy',Δz',1/Δt') = L_[x,y,z,t](1-((V²_[x,y,z,t]/C²)^1/2)or  in a 8 dimensional group taking the functions in coordinates right next to the variables such as (Δx',Δy',Δz',1/Δt')  Function of V(Δx,Δy,Δz,Δt) , This shows the 3+1 dimensions of Special relativity in a single equation for all of them as a function of velocity so they could be displayed as such which shows the relativistic killing vector field which is ☐(Δx',Δy',Δz',1/Δt'), This will give you a vector field like the one below by placing the relativistic coordinates over top the manifold of time-space but a four dimensional picture the below one is of a Black Hole like this.

 

 

Side note: Usually, I just ignore Moronium he doesn't understand Special Nor General Relativity too well and always is against it. For Moronium's Notice if you do this process you can find the every point that you plot exact state in relativity to each other simultaneously that is uniform by mathematically constructing the Time-space manifold with the light cones which killing vectors are E8 math, so it is "Real Universe's State".

Edited March 15, 2019 by VictorMedvil

[Moronium]

Killing vector group, eh?

 

In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric.  Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point on an object the same distance in the direction of the Killing vector will not distort distances on the object.

 

This condition is expressed in covariant form. Therefore, it is sufficient to establish it in a preferred coordinate system in order to have it hold in all coordinate systems.

 

...

if none of the metric coefficients is a function of time, the manifold must automatically have a time-like Killing vector.  In layman's terms, if an object doesn't transform or "evolve" in time (when time passes), time passing won't change the measures of the object. Formulated like this, the result sounds like a tautology....

 

 

 

https://en.wikipedia.org/wiki/Killing_vector_field

 

So it uses a preferred frame and says (tautologically) that the mere passage of time alone won't change an object's measure.  Well, now, aint that special?

 

1.  It aint got nuthin to do with Minkowskian spacetime.  The whole concept only applies to "a Riemannian manifold (or pseudo-Riemannian manifold)."

 

2.  "Co-variant" aint "invariant."

 

3.  Everything becomes much clearer when you adopt a preferred frame.  What else is new?  That said, SR absolutely prohibits the use of a preferred frame.

Edited March 15, 2019 by Moronium

[ralfcis]

I don't have the math ability to foray into the world of GR. All I'm trying to show is the obvious mistakes in the popular version of SR they're teaching out there. Namely, length contraction, the reason for age difference in the twin paradox (not being acceleration or a change in metrics but a delay of information during an imbalance of relative velocity), relativity's definition of time and its use of light signals to establish time, it's inability to establish age difference for scenarios that are not round trip, depiction flaws in the Minkowski STD, how the constancy of the speed of light really works and relativity's spacetime path rules. Pretty much everything in how SR is taught is wrong, including the meaning of E=mc² and the Michelson Morely results. Unfortunately no one out there can follow the algebra to see what I'm saying. I don't need 4-vector math to do so.

[Moronium]

 the reason for age difference in the twin paradox (not being acceleration or a change in metrics but a delay of information during an imbalance of relative velocity), relativity's definition of time and its use of light signals to establish time, it's inability to establish age difference for scenarios that are not round trip, depiction flaws in the Minkowski STD, . Unfortunately no one out there can follow the algebra to see what I'm saying. I don't need 4-vector math to do so.

 

No one needs needs a shred of math to know that the time I receive information can have NOTHING to do with your aging.  What if I just never look at you again?  Then what?  SR uses light signals in an improper way to establish clock synchronization, not time.

 

Likewise, as I already told you, SR does NOT require a round trip to make it's predictions.  That whole red herring only arises when some sophist is just making crap up as he goes along in an attempt to "prove" the ridiculous claim that, as between two given objects, "you can never tell who's moving."  It has nothing to do with the formal mathematical requirements of the LT.

 

Not that you'll ever understand any of that.

Edited March 15, 2019 by Moronium

[Moronium]

Likewise, as I already told you, SR does NOT require a round trip to make it's predictions.... It has nothing to do with the formal mathematical requirements of the LT.

 

 

Ralf, you've obviously been told lots of things about what SR is/predicts/implies, etc.  Many of those things contradict another.  Because you have no ability to reason for yourself, you don't, and can't, know what to believe.  Nonetheless you latch onto some of the crap you've been told as being unquestionably true. It is impossible to arrive at a coherent understanding under those circumstances.

Edited March 15, 2019 by Moronium

[ralfcis]

I'm going to answer your last question not for your benefit, because you didn't understand the answer the last few times, but because it's a fair question and maybe someone who tuned in late might benefit from the answer.

 

Reality is information and time is the rate of the flow of information. If the sun was knocked out of the sky, the reality of that event wouldn't reach us for 8 minutes. The max rate of information is c through time which manifests itself as the normal passage of time. Time can actually pass at any faster rate but to our perspective, the rate of time is maxed out at c.  Because information is delayed, there are two types of time and two types of reality. Perspective time is each of our individual perspectives of reality delayed by the speed of information. Relativity says that is reality instead of defining reality as the causal proper source of perspective reality  before it gets delayed.

 

 Proper time is independent of the speed of light delay and so being instantaneous can only be post-processed unless the participants are co-located. Perspective time is how we experience proper time in its delayed form or in its instantaneous form if it's local.  Proper time is independent of perspective and constant relative velocity so there is no time dilation in proper time. The time dilation that occurs in perspective time is independent of what's going on in proper time.  Proper time ticks at the same rate within all frames and between all frames in constant relative velocity. There are two exceptions. The rate of proper time is not common between frames under different gravity or experiencing 2 different relative velocities such as when info delay of constant relative velocity occurs due to one's change of velocity. Under those two scenarios, proper time is ticking at two separate rates between the two participants. 

 

The question is why would an imbalance in relative velocity cause proper time to tick at different rates between two participants? What is the link between velocity and time that would cause this? Nothing can travel faster than c and that includes the speed of information. That velocity is what creates both causality and time itself which manifests itself to us as the normal passage of time. Velocity controls the rate of that information transfer. The faster a ship goes out, the slower the rate of information that gets back to us and hence the slower we observe his time to be going from our perspective. This effect is reciprocal but is only perspective and not real from the causal reality definition. If he goes out at a constant velocity, the rate of time slowing from our perspective is also constant even though neither see their own time slowing because proper time is not slowing and they are co-located with that rate of time. Proper time rate is reality, not the illusion of perspective. 

 

We can see the illusion of time slowing by receiving his televised picture, he would appear to move slowly to us. If he was coming towards us, the rate of information from him would be increased to a faster constant rate. His televised picture would show him moving through time at faster than normal rate like a fast forward DVD.

 

This Doppler shift ratio is just as much an illusion as time dilation but is not the same thing as time dilation. Everything is always moving at c according to this equation:

 

c² = v² + v_t².

 

The faster you're observed to move through space, the slower you're observed to move through time. The time dilation is the other guy's observed velocity through time (v_t= c/Y) while the Doppler shift ratio is what we observe as the other guy's half speed velocity of (v_t). So numerically, if v = .6c, time dilation (1/Y) = .8 so v_t = .8c and the Doppler shift ratio is half speed of v_t = .5 (according to relativity's velocity combo law).

 

So none of this has anything to do with real ageing, it's all illusion of perspective; the two people are actually ageing at the normal rate. But if one makes a change in their velocity, an imbalance is caused in their relative velocity until the reality of the change reaches the other party which then establishes a new relative velocity between the two. Constant relative velocity is what causes time dilation between the two participants in perspective time but it has no effect in proper time. An imbalance in the relative velocity has a delayed effect, in perspective time, on the time dilation between them. Since Alice is co-located with her change in velocity, there is no delayed effect on her. She immediately sees Bob's new time dilation and Doppler shift ratio from her perspective. Bob's still going at the old relative velocity so he still sees Alice's old time dilation and doppler shift ratio until the delay of info between them is resolved. Reality is  information so Bob's perspective reality is out of sync with proper reality. 

 

If Alice was a GPS satellite orbiting earth, her orbit would be a round trip journey. Bob would not see any blip in his perspective of Alice's dilated time at her turnaround back to him. Unseen to him, in the realm of proper time reality, a correction is going on in their proper time rates. Alice is in fact ageing slower than Bob at a proper time rate that is not related to the time dilation factor, it is related to the Doppler shift ratio of her relative velocity to Bob which is the real relative velocity. Time is passing at twice normal rate for her while it still ticks at normal rate for Bob so she only ages 2 yrs for Bob's 4. Her velocity through time is actually 2c while Bob is still seeing it at .5c. This correction at the proper time level stops as soon as they re-establish a new relative velocity when the info reaches Bob that a change has been made. At this point, the Doppler shift ratio from Bob's perspective of Alice changes from .5c to 2c, they will now see each other go through time at double the normal rate but this is just an illusion of perspective time. In proper time, Alice was actually flying at double the speed of light through time for 4 of Bob's years (she did them in only 2 of hers).

 

Alice is unaware that she has been going at twice the velocity of light through time because she has only Bob to compare to. The moment she made her change, she saw his Doppler shift ratio switch to 2c from her perspective. The difference this time it was no longer perspective illusion but proper reality that she was going at 2c. She still saw herself as going at the normal time rate because her clock ticking would speed up along with her. Time itself had warped for her during this relatively short time in her journey. 

Edited December 26, 2019 by ralfcis

[Moronium]

Reality is the flow of information... there are two types of time and two types of reality. 

 

Nothing can travel faster than c and that includes the speed of information... causal reality that she was going at 2c. 

 

 

Heh, I see.  The great thing about having "two types of reality" is that the answer to every question is both yes and no.  You can never be wrong, no matter what answer you give.  Quite convenient, and yet not the least bit contradictory, I'm sure.

 

So much the better if you have 3, 4, or 5 realities.

 

I take comfort in one thing.  If North Korea launches a nuke at Hawaii, and Hawaii doesn't know it, then it can never hit them because it was never launched.  Not in "reality."  And even if it was dropped from 1 mile over Hawaii, it can still never land as long as the residents just don't look at it.  No information, no reality.

Edited March 16, 2019 by Moronium

[ralfcis]

You're confused at which one you can't see. Proper reality can only be seen instantaneously with perspective reality if the source of an event is co-located with the receiver of the news. Perspective reality is the only one each one of us experiences in the present. If the sun were to go out, we would have no advanced warning. We couldn't put a sensor on Mercury to tell us the sun went out because we'd see the light go out at the same time news of the sun going out reached us from Mercury. The speed of info is the speed of reality. Closing your eyes makes no difference. The reality is the sun was gone 8 minutes ago in proper reality but we still see it from our perspective reality until the news of its demise reaches us. What are the 3 or 4 other realities that you can imagine?

Edited December 20, 2019 by ralfcis

[Moronium]

. The reality is the sun was gone 8 minutes ago in causal reality but we still see it from our perspective reality until the news of its demise reaches us. 

 

Which one is really "real?"  Both?  Did the sun "really" go out, or does it depend on if YOU find out about it?

Edited March 16, 2019 by Moronium

[Moronium]

. What are the 3 or 4 other realities that you can imagine?

 

Given the endless contradictions, it's hard to count them all.

 

You say:

 

1.  Reality is information, and

2.  That nothing, including information, can ever exceed the speed of light.  OK, now what?

 

Now a brand new "reality" enters, one which says Alice is "really" traveling at 2c in "causal reality."

 

The difference this time it was no longer perspective illusion but causal reality that she was going at 2c.

 

 

At one point you say that "perspective" time is an "illusion."  It the next breath you say it is "reality."  

 

Which is it?  Or is there yet another "hidden reality" that says that both are true.  And one that says "neither is true?

 

You just make up "realities" as you go along, as contradictory as they might be.

Edited March 16, 2019 by Moronium

[Moronium]

As I've pointed out to you many times, if you want to claim that there is a "true" so-called "causal time," then from that point on all matters of mere "perspective" are absolutely irrelevant.  

 

Something you'll NEVER understand, because you have no conceptual understanding.  That, in part, is due to the fact that you simultaneously accept and reject SR, including whatever misinformation you have been fed about SR.  You are incapable of starting with the postulates of SR and making an independent assessment from there.

Edited March 16, 2019 by Moronium

[ralfcis]

Both. Proper reality causes perspective reality which is just delayed proper reality. Relativity only has perspective reality. So everyone's perspective is reality and the ordering of those perspectives in time depends on perspective. I think that assumption is a mess. They're just illusions of the one true proper reality. However, the universe goes to great lengths to ensure all those perspective realities can be traced back to the cause by bending proper time so that it syncs up again with perspective reality after the relative velocity imbalance time to ensure everything makes sense. It even finds a loophole in its max velocity rule by hiding the fact that Alice breaks the rule from both Alice and Bob. Alice is going at 2c through time but neither her on-board clock or comparing hers to Bob's Doppler shift ratio tells her she's moving through time at 2c. From Bob's delayed perspective, he only sees her moving at .5c until his perspective catches up with Alice's change and the Doppler shift ratio swings from .5 to 2 at t=8. It is looking back at this point that they could determine their clocks have a permanent difference and it's not reciprocal.

 

Relativity states that reciprocal time dilation is an example of travelling to the future ageing less years to get there. I say that's an illusion of perspective because both can't age less than each other. My story is recovery from relative velocity imbalance is the only true example of travelling to the future ageing less yrs to get there. I can't explain the physics behind it but I can show the math the physics must follow. Before relativity, the math would follow the physics and not vice versa.

 

PS. I'm impressed with your last question because it shows understanding on your part. My story is thin because I make it sound like the universe painted itself into a corner by setting a max velocity and causality and having to sneakily break its max velocity rule and bend time itself to preserve causality. 

Edited December 20, 2019 by ralfcis