Relativity And Simple Algebra

[Moronium]

When only two objects are involved SR mimics a preferred frame theory, alleged reciprocity aside.

 

If there are two objects, A and B, moving relative to each other, they will agree on their relative speed.  Say it's .8c.  Both will say that the other is receding from them at .8c, so they agree.  This will be based on doppler shift readings made by both.

 

Now look at two more objects, A and C.  C is receding from A in the opposite direction as B is.  Once again, A and C will agree on their relative speed.  No problems.  Let's say they both agree that their relative speed is, 8c

 

But now we effectively have 3 objects, not just two, and problems arise in SR.  We have B (going .8c to the east of A) and C (going .8c to the west of A).  If we want to determine the relative speed between B and C we no longer have any redshifts involving the A, the middleman.

 

So how does B see C?  One answer could be that they just don't see each at all, because they are separating from each at the relative speed of 1.6c and a signal from one can never reach the other.

 

Another possible answer is to cook up a math formula that says they see each other separating from themselves at the rate of only .975c.

 

But that's just math.  What doppler shift speed would they get if they actually measured the speed beteen them directly?  Both see themselves, on the basis of actual empirical measurements, traveling at a speed of .8c relative to A, so how can .975c possibly be the relative speed between the two of them?  Are all 4 of the separate prior  doppler readings, made by multiple parties, just wrong?  Does doing a math calculation somehow invalidate all those readings?

 

I asked Popeye which is right, .975c or 1.6c?  He said both are right.

 

And he says I'm a "science denier" who has entered the twilight zone if I even ask how B and C would see A if in fact the relative speed between them was only .975c.

 

But how is it possible for BOTH speeds to be right, as a matter of empirical fact?  Can anyone who is not in the twilight zone explain that to me?

 

One might note that saying that B and C are receding from each other at the rate of 1.6c does NOT mean that any one of the three is traveling at a speed exceeding c.  It would just mean that B and C don't see each other at all.

Edited February 23, 2019 by Moronium

[Moronium]

  Does doing a math calculation somehow invalidate all those readings?

 

I asked Popeye which is right, .975c or 1.6c?  He said both are right.

 

And he says I'm a "science denier" who has entered the twilight zone if I even ask how B and C would see A if in fact the relative speed between them was only .975c.

 

But how is it possible for BOTH speeds to be right, as a matter of empirical fact?  Can anyone who is not in the twilight zone explain that to me?

 

From post #267, above.

 

Anybody know the answer to that?

 

The idea that I can sit here at my desk and magically change the speeds of objects in the physical world merely by punching some numbers into a calculator, seems a little "unscientific" to me, somehow, ya know?

 

The idea that each of two mutually exclusive speeds are both right does too.  It means there are no reliable measurements to be had, no matter how sophisticated your equipment is. It also defies logic.

Edited February 24, 2019 by Moronium

[OceanBreeze]

[OceanBreeze]

Separation speed, as inferred by an observer located in the center of separation = 1.6c

 

Relative velocity between separating objects = 0.975c

[sluggo]

In addition to OB #247:

SR does not allow addition of velocity measurements from different frames.

If A and B  have a relative motion, their measurements of the velocity of D won't be equal.

There is one formula for velocity composition (since it involves the difference and the product of speeds).

With A moving at a, and B moving at b, A measures the relative speed of B as

(b-a)/(1-ab)

eg. (.8-.6)/(1-.48) = .38

Because of symmetry, B calculates the same value with a sign reversal

 

If A and B move in opposite directions at the same speed, the direction is important.

With A to the right and B to the left, A measures   the relative speed of B as

(-.8-.8)/(1+.64) = -.98

The gap between A and B is a spatial measurement, not bound by SR rules. 

[Moronium]

In the one-dimensional case, the velocities are scalars and the equation is either:

 

{\displaystyle \,v_{rel}=v-(-w)} \,v_{rel}=v-(-w), if the two objects are moving in opposite directions, or:

{\displaystyle \,v_{rel}=v-(+w)} \,v_{rel}=v-(+w), if the two objects are moving in the same direction.

 

 

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

 

The difference between velocity and speed is only significant when the displacement of position is different than the distance traveled.  In one dimension distance IS displacement.  The magnitude (speed) is the same by both measures.

 

You continue to make irrelevant "distinctions" while evading all questions, Popeye.  Can't you do better than that?  Semantic quibbles don't respond to the questions.  It's just a non sequitur.

Edited February 25, 2019 by Moronium

[ralfcis]

Ok I've finished my math exploration and the results are shocking even to me. Nothing of relativity remains, not even time dilation as anything but an illusion of perspective. I don't want the rest of the discussion to be about anything but the math, no more duelling dogmas and expert opinions from competing theories. So I've blocked anyone with opinions they can't support mathematically. That still won't guarantee dogma won't work its way in here because relativists would believe 2+2=5 if Einstein said so and would find a counter-intuitive way to justify that assertion. The evidence for that comes from my last post, where I outlined relativity supports two contradictory explanations for the pole in barn paradox (aka the ladder paradox), and not one relativist openly agreed relativistic math did not support the length contraction explanation. I don't know for sure that relativity is wrong, I just know the version fed to the masses is.

 

We'll begin again with the STD showing 2 depictions of .6c.

 

 http://www.sciencech...=6056&mode=view

 

If you follow any of the pink or yellow light signals from the number 2, they will all hit the number 4. The light travel time should give the guy at 4 an idea of what his age was when the guy at 2 sent the light signal to him. The answer should be the same in all cases because the results are independent of the infinite possible depictions of .6c relative velocity. As it turns out, the answers support relativity's contention that the present is dependent on perspective. The guy at 4 who receives the signal agrees in all cases that he was 2.5 when the sender was 2. 

 

Now anyone following the math would say that's not possible, the light signals all show different travel times so how can different times, subtracted from 4, all yield the same result of 2.5? Relativity does not give you the formulas on how to normalize the light signal travel times that are distorted by the depictions but I will. The length depicted must be multiplied by the doppler shift ratio. We'll go through the examples:

 

If the receiver is depicted as stationary (which is not the same as actually being stationary), the doppler shift ratio =1. The length of the pink line to the stationary 4 is 1.5 (yrs or ly, it doesn't matter) and multiplied by the DSR is still 1.5. The doppler shift ratio for the .6c depiction is .5 and the length of that yellow light line is 3 so 3 x .5 also equals 1.5. 

 

Now we could calculate the actual time length of the .33c light lines in the same way but we would lose some astonishing math relationships between half speed and full speed relative velocities. This part of the math discussion will lose everyone so if you're easily confused, don't read it because it will cause you to tune out of the rest of the discussion. 

 

.6c through space has a corresponding velocity through time of .8c (from the formula c² =v_x² +v_t² ). Half of .6c is .33c and half of .8c is .5c according to the relativistic velocity combo formula. .5 also happens to be the DSR at v_x=.6c; coincidence? not at all. The DSR is the scalar of the half speed of v_t.  Things get even more connected from here on:

 

.33c through space has a corresponding velocity through time of .9428 c (using the formula above once again). The half speed of v_t is therefore .7071c and the DSR is .7071 which is also the square root of .5 which was the DSR of v_x=.6c. The interconnections are staggering and like logarithms simplified multiplication, the interconnections between DSR, v_x and v_t greatly simplify their calculation for relative velocities other than .6c. Now you could go ahead and figure out the length of the light lines using geometry or graphically approximating them, but if you use the formula for (depicted length) x DSR = actual length, then you know the depicted length = 2.1213, the DSR = .7071 and the actual length as 1.5. So whatever the depiction, Minkowski or Loedel, the light lines are all the same length using DSR to normalize them.

 

Ok, so now we can determine the actual length of the light signals to give the same perspective time for any relative velocity depicted in any way. More importantly I'm going to show how the light signals can be used to show how Bob and Alice are actually the same age in proper time which is not subject to perspective. To put numbers to it, the answer should be that if they both  sent their signal when they were 2 (proper simultaneity), the receiver should interpret that he was also 2 in proper time when the signal was sent. So now comes part 2 of the conversion to proper time.

 

Just as the light signals must be normalized by the DSR, the time readings must be normalized by gamma (Y). From the perspective of the "stationary" Bob, (ct)² = (ct')² +(x/c)² . For example at t =2.5, t'=2 and x= 1.5 and plugging in these values into the formula yields the correct results. But from Alice's perspective, t and t' switch places in the equation and x must be divided by Y to give the correct results. (Notice this is not the same as the formula for length contraction.) So the correct formula is (ct)² = (ct')² +(x/(cY))² for all perspectives.

 

I have to stop for now 

Edited December 19, 2019 by ralfcis

[Moronium]

The difference between velocity and speed is only significant when the displacement of position is different than the distance traveled.  In one dimension distance IS displacement

 

This is really an irrelevant red herring, but to illustrate:

 

1.  At the Indy 500 a car drives (in an oval) for 2.5 hours and his average speed is 200 mph.  However his velocity is 0, because all he does is end up at the same place where he started, i.e., the start/finish line. His displacement is 0 in that case.

 

2.  The same car drives a 500 mile distance in a straight line in 2.5 hours.  Now his speed is again 200 mph.  But now his velocity is ALSO 200 mph.  They are the same, because the displacement is the same as the distance, i.e., 500 miles.

 

In case 2 there is simply no practical or meaningful difference between speed and velocity.  His speed, relative to the ground, is 200 mph and his velocity, relative to the ground, is 200 mph.  Relative speed = relative velocity.

 

And that would all be true whether he was driving north, south, east, or west.  The "direction" changes nothing either.  That would only be a factor if he is changing directions.  Traveling in a straight line (one dimension) precludes any change of direction.

 

Once again, in such cases relative speed = relative velocity.

 

Likewise, chanting the mantra that "velocity is not speed" or capitalizing the word VELOCITY, does not change, explain, or answer anything.  You seem to think it does, somehow, Popeye. God only knows why.  You seem to think you are giving substantive responses by doing that, but you're not.

 

For that reason, posting a picture to "prove" that speed is not velocity does not prove any relevant point.  Nobody said otherwise, certainly not me.  No one's arguing that, so there is no "point" to make.  It's just not relevant in the case we're considering. that's all.  It is a distinction without a difference.  Speed and velocity are the same things here.

 

The reason for invoking the velocity addition formula here, as questionable as it may be, has NOTHING to do with the difference between speed and velocity.

Edited February 25, 2019 by Moronium

[Moronium]

So how does B see C?  One answer could be that they just don't see each at all, because they are separating from each at the relative speed of 1.6c and a signal from one can never reach the other....

 

One might note that saying that B and C are receding from each other at the rate of 1.6c does NOT mean that any one of the three is traveling at a speed exceeding c.  It would just mean that B and C don't see each other at all.

 

This is not the primary question in this post, but it does lead me to ask whether the velocity addition formula should even be applied at all in these circumstances.

 

Why presuppose that B MUST "see" C?  That doesn't seem consistent even with SR.  If we point a telescope in the sky and see something moving away from us at .8c, then point it in the opposite direction and see another just like it, do we assume that light from one is reaching the other?  I don't think so.  Is anyone even sure that the formula applies here?  I aint.   If so, why? 

 

One problem that can arise when someone is mechanically relying on a formula as a basis to declare "how the universe works" is knowing when to apply it.  It may apply in some circumstances and not others.

 

But even in a case where it is clear that it is being properly applied, the primary questions would still be:

 

Does doing a math calculation somehow invalidate all those readings?...

 

How is it possible for BOTH speeds to be right, as a matter of empirical fact?  Can anyone who is not in the twilight zone explain that to me?

 

Edited February 25, 2019 by Moronium

[Moronium]

This is an excerpt from a foreign physicist who was invited to present it at 10th International Symposium Honouring Mathematical Physicist Jean-Pierre Vigier, At PortoNovo, Italy, in 2016.  Seems the velocity addition formula is taking a little heat from from modern physicists, eh?  Lots of math in it, too!

 

The Velocity Addition Formula According to Special Relativity — The Most Unsustainable Formula in All Physics

 

When  the  velocity  addition  formula for  special relativity  is  reviewed  from  the  perspective  of  its derivation, it is concluded that it is rhetorical tautology. It  is  rhetorical  tautology  also  within the  theory  of special relativity itself which means that even if this theory  pertains,  the  velocity  addition  formula according this theory cannot pertain. This conclusion is supported with an analysis of its functional aspect and it can be seen  that  it does  not hold  true either algebraically or physically at the level of the velocity addition formula in relative motion.

 

https://www.researchgate.net/publication/312938573_The_Velocity_Addition_Formula_According_to_Special_Relativity_-_The_Most_Unsustainable_Formula_in_All_Physics

 

"The Most Unsustainable Formula in All Physics?" I don't see how its even possible to question the formula.  It's math, dammit!  It has to be true.  

Edited February 26, 2019 by Moronium

[OceanBreeze]

I got my dark sunglasses,

 

I'm carryin' for good luck my black tooth

 

Don't ask me nothin' about nothin'

 

I just might tell you the truth

 

[ralfcis]

Jeez it seems the most important part of this thread is in trying to explain why 2+2=3 and not trying to understand why   2+2 does not equal 5. Yes 2+2 adds up to a relative velocity that is less than the straight sum of the two velocities. That's the relativistic combo law and you can debate its validity from now until the end of time. I support it, others don't. I hope that ends the pollution of this thread. Can't Moronium get his own physics sub-forum where he just posts wiki articles all day long? Why does this have to happen on the topics I'm trying to explore?

 

What I'm attacking here is the idea that 2+2=5; the idea that at .6c when Alice is 4, Bob is 5 and vice versa in perspective time. I'm trying to prove 2+2=4; at .6c, when Alice is 4, Bob is also 4 in proper time. Yet there is not one comment or question or agreement or disagreement on this more important topic. Obviously I haven't made it worth anyone's time to try to understand the math. No one really wants to find out if relativity's broken because it seems to be running just fine on 4 flat tires and if it ain't really broke, why fix it, just ignore the flats and the facts.

Edited December 19, 2019 by ralfcis

[Moronium]

That's the relativistic combo law and you can debate its validity from now until the end of time. I support it, others don't.

 

If you accept the velocity addition formula, and you believe that .8 + .8 = .975, then why would you have any problem accepting any other math, no matter how bizarre, you see in SR?

 

If you're trying to prove that they age equally, good luck.  It aint gunna happen in SR or any other theory which rejects the experimentally proven fact that clocks do slow down with increased speed.

 

SR is broken, beyond any possibility of repair.  It's not a question of fixing a flat tire, it's been totaled. There are other theories which avoid all it's contradictions, but you refuse to even look at them.

 

As they say, "You made your bed, now lie in it."

Edited February 27, 2019 by Moronium

[Moronium]

Don't ask me nothin' about nothin'

 

 

Typical response, but one that I didn't expect from Popeye.  It's not the least bit unusual for the SR faithful to show disdain for anyone who questions them.  When they make weak, easily refutable arguments in support of SR which fall apart, they just call you a crank and a science denier and refuse to even entertain any more questions.

 

I swear, you couldn't find a bible-thumping fundy who had more faith than an SR disciple.  

 

And, like them. they have even more faith than their progenitors did.  I hear-tell that even Jesus asked why God had forsaken him.

 

They say you should never argue about politics or religion.  They should have included science in there.  Then again, maybe there's no difference, at least not with those who adopt their version of "science" as a religion.

Edited February 26, 2019 by Moronium

[Moronium]

If there are two objects, A and B, moving relative to each other, they will agree on their relative speed.  This will be based on doppler shift readings.  Let's say those readings show a relative speed between A and B of .8c.

 

Now look at two more objects, A and C.  C is receding from A in the opposite direction as B is.  Once again, A and C will agree on their relative speed.  No problems.  Let's say they both agree that their relative speed is also 8c.

 

So how does B see C?  

 

[One] possible answer is to cook up a math formula that says they see each other separating from themselves at the rate of only .975c.

 

Does doing a math calculation somehow invalidate all those readings?

 

I asked Popeye which is right, .975c or 1.6c?  He said both are right.

 

 

Since no one else will, I'll answer this myself.

 

Pulling out a slide rule and playing with it for awhile does not, and cannot, change the speeds of objects in the real world.

 

To the extent that you want to argue that B and C only "see" each other that way, then so what?  What do delusions have to do with physics?

 

The claim that they are "both" right is also impossible as both a physical and logical matter.

 

Christians believe in miracles which defy all known laws of physics.  So do SR adherents.  There's just a different "holy savior," in those two metaphysical positions that is capable of performing miracles.  For the devout SR disciple the savior is math.

Edited February 27, 2019 by Moronium

[Moronium]

Pulling out a slide rule and playing with it for awhile does not, and cannot, change the speeds of objects in the real world.

 

If you could ever realize that, Ralf, then you would at least be taking a little baby step towards finding reasonable answers to the questions you are asking.

Edited February 27, 2019 by Moronium

[ralfcis]

In later posts I completely abandon this method as being a mathematical shortcut to the correct answer. It does not reflect the physics that is actually going on. Age difference is not a result of time dilation becoming reality by adding t_x  to the person's age who makes a velocity change. This method pertains only to how light signals can be used to convert the perspective time on each of their watches into proper time. You can skip this.

 

Ok so far we've established the normalization formula for light travel time for the Loedel depiction and Minkowski depiction of .6c relative velocity. (The Loedel is two .33c lines leaving earth in opposite directions and the Minkowski is only 1 line at .6c leaving an earth depicted as stationary.) Some doubt .33c + .33c = .6c but they are still in grade school and haven't caught on to the new math (relativistic addition). The light travel times were all depicted as having different travel times but with the normalization equation, all light lines sent out from proper time tau =2, are received at proper time tau=4 and take 1.5 proper time to propagate no matter how the .6c relative velocity is drawn. 

 

Now if I want to take perspective out of the equation, there is .5 yrs unaccounted for. I'm saying if either bob or alice send out a light signal at proper time tau = 2, either one should be able to calculate they were both proper time tau=2 using the light signals. Instead, if they receive the light signals, they calculate their perspective time of t=2.5 for when the sender was t=2. 

 

That discrepancy arises out of the time equivalent t_x of the distance between them. I'll save you the derivation and the formula is:

 

t_x = t'(Y_m-1) where Y_m is the Y in the minkowski depiction.

 

Let's do some examples:

 

In our example whether Loedel or Minkowski, t'=2, Y_m=1.25 so t_x=.5. In proper time both bob and alice are 2 but in perspective time you add tx to the perspective you want to calculate. From bob's perspective, t= tau + t_x which means Bob=2.5 and alice =2. From alice's perspective, she's 2.5 and bob is 2 because you add t_x to alice's tau.

 

Another example would be both bob and alice leaving earth at .6c in opposite directions. The minkowski equivalent is alice leaving a stationary earth at .8824c (=.6c+.6c). Y_m = 2.125 and at t'=2 (when a light signal is sent) t_x = 2.25. So the proper time for both is tau=2 but from Bob's perspective he was 4.25 when alice was 2 using the light signal lines and from alice's perspective she was 4.25 when bob was 2 using the light signals to establish their perspective and proper (both tau=2) time ages.

 

So what does this do for us? Well it eliminates relativity's concept of reciprocal time dilation as being real (it's just an illusion of perspective). It also eliminates relativity's concept of age difference. Let's see how it does this in the classic example of alice doing a round trip at .6c turning around at t'=4. So we use our new formula where Y_m =1.25 at t'=4 so t_x=1 for the outbound leg. It's the same result for the inbound leg for a total of 2 yrs distance equivalent time. Since Alice did the velocity change, we are looking from Alice's perspective so 2 yrs gets added on to Bob's  tau = 8. So he is 10 and alice is 8. If Alice had kept going and not turned around, from Bob's perspective at t'=4, he would have been 5 but from Alice's perspective when her and Bob's tau=4, her time is 5. 

 

There are no fancy-shmancy spacetime path rules or Rindler metric vs Minkowski metric, just normalized light signals, time equivalence to distance separation and recognition that depiction of relative velocity is irrelevant to the results.

 

Now you can simply answer what time is it but you have to ask do you want the proper time or the perspective time and from which perspective. Relativity did not allow such a simple question to be answered until the valid end of a spacetime path.

Edited December 19, 2019 by ralfcis