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Relativity: Coming to Terms 3: Gamma Velocity

03/26/2016 9:56 AM

Repost of a thread that was not deleted by admins

You won't find the term "gamma velocity" (Yv) in any relativity text but I think it should be because it clears up many misconceptions about relativity. The popular idea that nothing can travel faster than light needs clarification and that's where Yv comes in. It's all about perspective. There is no time dilation or length contraction within your own timeframe, those only exist when each reference frame perceives the other. Any velocity outside your own is a vector through spacetime with a component through space and another through time.

We can only perceive the component through space as velocity and that component is limited by the speed of light. As a spaceship goes closer and closer to the speed of light, more and more percentage of its velocity vector goes into the time dimension as slowed time but not slowed velocity. This is an important distinction that confuses many into thinking that if time is slowing then velocity must be slowing as well. But how can we reconcile the ship's great velocity and relativity's call that time must be slowing to near zero for the ship?

Well, our time must be relatively flowing at a near infinitely fast rate as seen by that ship even though, from our perspective, we see time ticking for us at its normal rate. As we look up at the ship going near c, generations of us would be turning to dust watching it. Our rapidly flowing time is compensating and masking the ship's outward slow time.

We only see velocity v through space but the ship is actually going Yv through spacetime (where Y=1/sqrt(1-v2/c2)). If a ship could reach near c, a normal time rate would be passing within the ship from the ship's perspective, but outside the ship we would be aging rapidly and we would see people inside the ship aging very slowly.

This aging imbalance is how the unseen velocity component through the time dimension manifests itself and how the people within the ship would age very little in their timeframe in a trip across the universe. We, on the other hand, would not survive their journey; we'd be long dead by the time they returned. From our perspective, they never exceeded the speed of light because if they traveled a distance of a million light years, it took a million of our years for them to do it.

From their perspective, they never exceeded the speed of light, despite the huge distance they traveled in very little of their time, because their time is basically suspended even though it runs at normal rate from their perspective. They traveled those great distances, frozen in time, as though they were in suspended animation from our perspective.

The light that began with them at the start of their journey would beat them to the finish line. Even though we may have seen them moving very slowly within the ship (if they ran from side to side within the ship we'd see them run at normal speed because there is little relative velocity in that direction so no time dilation just as there is no length contraction), both we and they would see any lights turned on within the ship propagating at full light speed, unaffected by the slow time. Why? Why is energy not subject to the effects of relativity the same way matter is?

This phenomenon does not happen to light itself because it has no velocity component in the time dimension, it travels at full light speed through space only. The popular idea that light travels the universe instantaneously because it sees the universe length contracted to zero is completely false. The photon does not materialize simultaneously at both its source and destination, it takes exactly as long to travel from its perspective as from our perspective because no time dilation is involved.

None of the light speed vector appears in the time dimension. If light followed the same rules as matter, its frequency would appear stopped at zero from our perspective. Frequency is no different than ticks of a clock and if time was slowing it should manifest itself as slowed frequency. But it's not, we can measure its speed and frequency in the space dimension which is accessible to us.

We can even capture Raskar photographs of light propagating and there is absolutely no length contraction seen in light pulses. I don't know why there is this sharp difference between how energy waves propagate and how particles propagate, why is travel through the time dimension not allowed for energy? The answer to this question would shed quite a light on the nature of spacetime except that no one bothers to ask this question.

In another section I'll show how Yv negates the concepts of relativistic mass and length contraction both of which people consider real. I'll also define what "real" is.

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#1

Re: Relativity: Coming to Terms 3: Gamma Velocity

03/28/2016 3:32 AM

I don't fully follow the concepts you are putting across. Posts a bit long? But I like your persistence, keep it up.

Regards JD.

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Re: Relativity: Coming to Terms 3: Gamma Velocity

03/28/2016 8:35 AM

Thanks, I've been told by many that my persistence is my least endearing quality.

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#3
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Re: Relativity: Coming to Terms 3: Gamma Velocity

03/28/2016 10:38 AM

"...persistence is my least endearing quality."

Yeah, I think I read that somewhere.

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Re: Relativity: Coming to Terms 3: Gamma Velocity

04/01/2016 11:07 AM

Not that anyone cares, and believe me I prefer it that way, I'd like to go through the math for Yv and show what pops out:

v=x/t, simple formula for velocity. Multiply both sides by Y.

Yv=Yx/t, plug in the formula for length contraction x'=Yx.

Yv=x'/t, An example of this is the length contracted distance muons travel to the surface of the earth in their half life time we would measure in a lab on earth. That's also the time they take to cross the contracted distance.

Now plug in the formula for time dilation t=Yt' into Yv=Yx/t:

Yv=Yx/Yt'=x/t', An example of this is the distance we see muons cross from the upper atmosphere to earth in the time we see as slowed for them (which is their half-lifetime in our lab multiplied by Y). Their half-lifetime has been increased by Y which gives them enough of our time to cover the distance we see them cover. The half-lifetime for them is unchanged and smaller from their perspective.

So we see their time slowed (or increased) and they see our distance contracted. The tricky part to understand is that both time dilation and length contraction are reciprocal in perspective. The muons also see our time slowed and we see their length contracted much like distance perspective where a guy in the distance sees us shorter and we see him shorter.

Anyway, the point is whether you want to consider length contraction or time dilation, it all depends on whether you group Y with distance or time in the Yv equation so they're 2 sides of the same thing.

More math:

So if Yv is the velocity vector through spacetime and the x-axis is the light speed limited velocity through space, then what is the y-axis, the unlimited velocity through time?

We'll call it w for now and using Pythagoras we get the formula Y2v2=v2+w2. Those 2's mean squares.

So w2=v2(Y2-1). Using Y2=c2/(c2-v2) we get

w2=v2(c2-c2+v2)/(c2-v2) which reduces to

w2=v2(v2/(c2-v2). Take the sqrt of both sides and multiply the right side by c/c:

w=v/c *(vc/sqrt (c2-v2) where c/sqrt(c2-v2) =Y which reduces to

w=v2Y/c. This is the velocity component through time that we on earth can't see from our perspective on earth. We can only see the velocity component through space. As that component gets closer and closer to c, the velocity component through time gets closer to infinity.

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