Relativity & Quantum phenomena (updated)

This is a revision of a blog-post that was published on September 24, 2011. There have been only minor modifications, especially on the mathematical formulas.

It is well known that according to the Einstein’s Special Theory of Relativity the maximum speed that is possible to occur is the speed of light in vacuum. This is an almost universally accepted principle among modern physicists.

A recent experiment has produced a result that shocked the scientific community. The Opera neutrino experiment has measured the speed of neutrons traveling from CERN to Italy higher than that of light. This result is unacceptable according to the well grounded, both theoretically and experimentally, theory of relativity. Even the scientists who performed the experiment doubt about their own result. They ask from the scientific community to scrutinize the experiment in order to detect any errors.

From my point of view, there is no error. This is a result that I suspected and expected many years ago.

What made me doubt the limit of the speed of light is the particle/wave duality of very light (mass-wise) particles. As I suspect, since I have no means to perform measurements, the speed c is the speed that the information travels (through light or other medium). A particle of very little mass, even though it can receive enough energy to increase its speed beyond c, that speed cannot be measured, since the medium that measures the speed has its own limit. But still, the particle absorbs this energy and instead of increasing its speed, it is supposed to increase its mass. After all, a particle with a mass m that moves with speed c has a kinetic energy E=\frac{1}{2}mc^{2}. If the particle absorbs more energy then, since it can’t (?) increase its speed, it should increase its mass (this I doubt).  The absorbed energy is not possible to disappear.

But what happens if and when a particle increases its speed beyond the speed of light c? (if that’s possible – big if) Or as I understand it, beyond the speed of the medium that carries information.

I expect that when an object moves faster than light, lets say λ (λ ͼ R, λ>1) times faster than light (velocity: v=λ·c) in a line with a distance h from the observer (frame of reference) then the following would occur:

position at t=0:  x=-x0, y=0 (for simplicity), z=h

The information of the position at t=0, will reach the observer at Δt = \sqrt{x_{0}^{2}+h^{2}}

Now this is the interesting part: There are two given positions, lets call them A (x=x_{A}<0,\; y=0,\; z=h) and B (x=x_{B}<0,\; y=0,\; z=h), with |x_{A}|>|x_{B}| that the object appears to the observer to occupy concurrently!

This happens because the time that light takes to travel from A to O (observer: x=y=z=0) is equal to the sum of the time that the object moves from A to B with a speed v=λ·c>c, plus the time that the light takes to travel from B to O (with a speed of c, of course). This is possible because B is closer to the observer at O, than A, thus light (or information) requires less time to travel to O and the remaining time is enough for the object to travel from A to B with a speed v=λ·c>c

This means that:

Δt(AO) = \frac{\sqrt{x_{A}^{2}+h^{2}}}{c}

\vartriangle t(AB)+\vartriangle t(BO)=\frac{|x_{A}|+|x_{B}|}{\text{\ensuremath{\lambda}c}}+\frac{\sqrt{x_{B}^{2}+h^{2}}}{c}=\frac{x_{B}-x_{A}}{\lambda\cdot c}+\frac{\sqrt{x_{B}^{2}+h^{2}}}{c}\quad\left(x_{A}<0\;,\; x_{B}>0\right)

Δt(AO) = Δt(AB)+Δt(BO) <=>

\Longleftrightarrow\frac{\sqrt{x_{A}^{2}+h^{2}}}{c}=\frac{x_{B}-x_{A}}{\lambda\cdot c}+\frac{\sqrt{x_{B}^{2}+h^{2}}}{c}\Rightarrow

\Rightarrow\lambda=\frac{x_{B}-x_{A}}{\sqrt{x_{A}^{2}+h^{2}}}-\sqrt{x_{B}^{2}+h^{2}}

So, a body moving with a speed v=λ·c, will appear to an observer at point O as existing at two different points A and B at the same moment. And there is no way to find out which one is the true spot, since both spots are equally real. A different kind of uncertainty…

Between the points A and B, the observer perceives a wave-like behavior from the particle.

I couldn’t be more unsure about my thoughts. I can’t check and see whether they are right or wrong, since I can’t afford anything like a particle accelerator!

As is written on the blog title, these are just thoughts on a screen.

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UK and EU

Yesterday, December 9, 2011 the prime minister of the UK refused to coordinate his country with the rest of the European Union.

This decision has been mostly interpreted as a permanent separation of Britain from the rest of Europe. It is certainly a separation when a single country defies the will of everybody else. But not permanent.

David Cameron chose wisely. This decision deprives all countries from their ability to set their own fiscal policy and gives almost absolute power to a central economic coordinator that is not democratically elected. David Cameron chose to avoid to associate the economic policy of UK with the EU. Either way, the problems are huge.

Germany and France wish to keep the Euro as high as possible and deny that their policy has forced a downward recessional spiral due to a reduced monetary supply. The European Central Bank has very limited power compared with the corresponding Fed in the USA. The Americans have followed the one and only prudent way: “print” money. It’s interesting that two opposing financial theories, those of John Maynard Keynes and Milton Friedman, provide the same solution. Increase the supply of money. According to Keynes, the extra money would force the balance of the economy to increased production, especially if they are invested by the state itself and directly increasing the purchasing ability of the lower classes. According to Milton Friedman, the money supply should be canalized to the banks, in order to leave the private sector make the best choices.

I don’t intend to point which is the best approach (although I do agree with Keynes) but to set clear that the solution is at the Federal level. While Germany and France constrain the financial power of the ECB, the recession spiral will not end.

The British choice is to keep their options open. They are not constrained by the fiscal restrictions of the recent agreement and can use the advantages of being able to shape their own monetary policy. The Euro is a currency in trouble. If the Eurozone countries manage the situation and make it attractive in the future, nothing forbids the UK from adopting it. But now, this option is not attractive at all.

Relativity and quantum phenomena

It is well know that according to the Einstein’s Special Theory of Relativity the maximum speed that is possible to occur is the speed of light in vacuum. This is an almost universally accepted principle among modern physicists.

A recent experiment has produced a result that shocked the scientific community. The Opera neutrino experiment has measured the speed of neutrons traveling from CERN to Italy higher than that of light. This result is unacceptable according to the well grounded, both theoretically and experimentally, theory of relativity. Even the scientists who performed the experiment doubt about their own result. They ask from the scientific community to scrutinize the experiment in order to detect any errors.

From my point of view, there is no error. This is a result that I suspected and expected many years ago.

(I’m not trying to be a wise guy! Just trying to lay down my own concerns)

What made me doubt the limit of the speed of light is the particle/wave duality of very light (mass-wise) particles. As I suspect, since I have no means to perform measurements, the speed c is the speed that the information travels (through light or other similar mean). A particle of very little mass, even though it can receive enough energy to increase its speed beyond c, that speed cannot be measured, since the medium that measures the speed has its own limit. But still, the particle absorbs this energy and instead of increasing its speed, it is supposed to increase its mass. After all, a particle with a mass m that moves with speed c has a kinetic energy E=(1/2)mc^2. If the particle absorbs more energy then, since it can’t (?) increase its speed, it should increase its mass (this I doubt).  The absorbed energy is not possible to disappear.

But what happens if and when a particle increases its speed beyond the speed of light c? (if that’s possible – big if) Or as I understand it, beyond the speed of the medium that carries information.

I expect that when an airplane (or something) flies faster than light, lets say λ (λ ͼ R, λ>1) times faster than light (velocity: v=λ·c) in a line with a distance h from the observer (frame of reference) then the following would occur:

position at t=0:  x=-x0, y=0 (for simplicity), z=h

The information of the position at t=0, will reach the observer at Δt=sqrt(x0^2+h^2)

Now is the interesting part: There are two given positions, lets call them A (x=x[A]<0, y=0, z=h) and B (x=x[B], y=0, z=h), with |x[A]|<|x[B]| that the airplane appears to the observer to occupy concurrently! (Although the same could be valid for x[A]<x[B]<0 and v=λ·c>c>0)

This happens because the time that light takes to travel from A to O (observer: x=y=z=0) is equal to the sum of the time that the plane moves from A to B with a speed v=λ·c>c, plus the time that the light takes to travel from B to O (with a speed of c, of course). This is possible because B is closer to the observer at O, than A, thus light (or information) requires less time to travel to O and the remaining time is enough for the airplane (or particle, or anything) to travel from A to B with a speed v=λ·c>c

This means that:

Δt(AO) = sqrt(x[A]^2+h^2)/c

Δt(AB)+Δt(BO) = (|x[A]|+|x[B]|)/(λ·c) + sqrt(x[B]^2+h^2)/c = (x[B]-x[A])/(λ·c)  + sqrt(x[B]^2+h^2)/c    (x[A]<0 , x[B]>0)

Δt(AO) = Δt(AB)+Δt(BO) <=>

<=> sqrt(x[A]^2+h^2)/c = (x[B]-x[A])/(λ·c) + sqrt(x[B]^2+h^2)/c =>

=> λ = (x[B]-x[A]) / [ sqrt(x[A]^2+h^2) – sqrt(x[B]^2+h^2) ]

So, a body moving with a speed v=λ·c, will appear to an observer at point O that exists at two different points A and B at the same moment. And there is no way to find out which one is the true spot, since both spots are equally real. A different kind of uncertainty…

Between the points A and B, the observer perceives a wave-like behavior from the particle.

I could never be more unsure about my thoughts. I can’t check and see whether they are right or wrong, since I can’t afford anything like a particle accelerator!