Is The Neutrino A Tachyon?

We have all heard of the hypothetical particles called tachyons. They have a rest mass M that also has an imaginary value (M2<0). It turns out that (E=gM), the observable mass-energy of these light weight particles, becomes ''real'' and ''positive''.

If a particle was able to defy the light-speed barrier so that v was greater than c (v>c), then both g and E would become imaginary quantities, because ß would be larger than 1 and (1 - ß2) would be negative.

When using imaginary concepts, we must use complex numbers... nothing too complex about them, so don't be scared off! We need the calculus in concepts that are imaginary - not quite existing in the realms of the real - but are ''real'' nonetheless... we use it when calculating the imaginary dimension of time, and even concepts beyond ''c'' - imaginary mass.

To understand this better, we must consider the pyhagorean theorem.Complex numbers deal with square roots. Now, you might remember square roots from high school. A number that is multiplied by itself produces the square root - thus, the square root of 4 is (2 x 2). The square root of 9 is (3 x 3). The square root of 16 is (4 x 4), ect. Note however, that the square root of 1, is (1 x 1). Complex numbers move into the negatives; thus, it helps mathematicians work out the improbable square root of -1, for instance, which is 'i' x 'i' = -1. The 'i' stands for ''impossible'', and it helps us in calculating numbers that are not in the real world.

Another example is the square root of 4, which is (i2)^2 = -4. Quantum Physics and Relativity would be impossibility, without complex numbers, and so would our ability to calculate time as an imaginary dimension of space.

In a standard course of geometry, one will inventually learn the pythagorean theorem. As you will probably know, the theorem applies to length of the right sides of a right triangle.

It is a simple formula, and it tells us that if one was to work of the angles on the sides of the triangle, the sums of two of those angles will equal the sum of the remainding value angle. We say that the third angle is the one raised on the hypotenuse. The formula is:

a^2+b^2=c^2

The sides of the triangle are similar based to how we work out the lengths of space and time. Because time is a universal invariant, we say that the imaginary time dimension is an invariant relationship.

If we apply this triangle as an invariance of space, we find some interesting results... explanations to why time is relative and why we move so very slow through space, and so very fast through time; or it can be seen that time moves through is very fast - at the speed of light actually.

If you regard time as a dimension of space, you create, according to Minkowski, right triangles with one side adjacent corresponding to time and the other to space. Both legs of the space triangle remain in in ''real space'', whilst in the time triangle, its legs remain in ''imaginary space.''

So long as the imaginary side of the triangle remained longer than the real side, the hypotenuse will have a ''timelike'' order... But if one speeds up, then the traingle becomes warped, and if we where to reach ''c'' then both sides become exactly the same. In this sense, time stops and you aren't really moving at all!

If you exceed this value, then the real leg becomes longer than the imaginary leg, and you are now oscillating through the time dimension. This is what we mean by speeds that are bradynic, photonic or tachyonic. There is a boundary created at ''c'', and this is highlighted through the spacetime triangle.

Now, it has come to light (mind the pun) on the mass of the electron neutrino (Ve), because it is a leading "dark matter" candidate... and we don't know the phsycial properties of dark matter. We have some examples of what some dark matter might be like, such as the axion particle which travels through material objects!

We can create neurtino's from the decay of tritium. The basic underlining rule is through the relativistic realtion between energy and momentum E^2 = P^2 + M^2... and we work out that it is mass squared that works out the neutrino mass from tritium decay... but this mass squared can be seen in light of either a positive reult or a negative result, and if it is a tachyon, containing a very light weight amount of imaginary matter of about i × 12 eV, there is the big problem that nothing fuitful will arise out of this... because the theorists do not believe its qualities would be observable or known.

But, i assume, that if we could harvest neutron energy, and also assuming that it is made of this imaginary stuff, then it might have profound implications for fuel... It might even produce the first spaceship that can jump into hyperspace!

 

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... and ofcourse, i meant to say, ''that is we could harvest neutrino energy,'' not ''neutron energy...'' that was a sloppy mistake.

 

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A long time ago, there was a research group who proposed trying to generate & detect tachyons, which are not neutrinos.

It is alleged that particles traveling faster than light will generate Chernkov radiation, which I beleive is blue. I think this has been verified for particles traveling faster than light can travel in some medium other than a vacuum.

At the time Martin Gardiner wrote a Mathematical Games each month in Scientific American. He was very knowledgable in physics as well as mathematics, and I believe that he was responsible for the demise of the research project.

Martin pointed out that the equations relating to Tacyons predicted the following (among other properties).

• As mentioned above tacyons would generate Cherenkov radiation in a vacuum.
  
  
• Adding energy to tacyons slowed them down with the velocity of light as the lower bound.
  
  
• As tachyons lost energy they speeded up. I am not sure if there was an upper bound to the speed (probably not).
  
  
• Tachyons travel backwards in time.

Martin pointed out that if some process generated tachyons at noon, the radiation would be visible before noon since the tacyons travel backwardx in time. When observed, the researchers could decide not to initiate the process, creating an unacceptable paradox.

It is my understanding that the above analysis resulted in the demise of the research and a general consensus that tachyons will never be generated by any process.

 

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How can anybody ever know if tachyons travel back in time ??

 

Imaginary, surely?

It's one or the other...

 

It's a tardyon, like a lot of the participants in this forum.

 

I assume you mean the time-reversed complementary particle, the re-tardyon?

 

Enmos: My information is second hand. I never studied the pertinent relativity equations, having merely read articles by people who did study the equations..

I think that Special Relatvity applies, in whiich case the equations should not be hard to understand. Once upon a time I understood other SR equations while taking a course. If General Relativity is involved, forget about studying the equations. They are really difficult to understand.

What I have read claims that the pertinent equations indicate time reversed pathes for tachyons as well as reversed energy requirements.

The potential paradox is viewed as indicating that the equations do not relate to reality.

The equations have a singualrity at the speed of light. When approached from below, more and more energy is required to increase the speed of an ordinary particle. When approached from above, more and more energy is required to decrease the speed of a tacyons. Neither case allows reaching the limit.

 

Thank you everyone for involving in this discussion. I'll be able to answer everone when i have a bit more time. But first, hey Oli.
I know its imaginary, but i prefer to call them ''impossible numbers,'' simply because they deal with calculations that are based upon idea's which are impossible for intuitive thought. It is the ''improbable calculation of the square root of -1.
... No, in this sense we must keep ''universal invariant'' and ''relative'' conceptes seperate. When we speak of invariant relationships, there are many in physics, but when i speak of a universal invariant, i mean that times relationship throughout space can never be removed, it is an invariant of space; relative speeds just shows that time is not very isotropic at all with differential times for different gravitational fields of force.

Reiku :m:

 

quantum world seems so distant to me...when all of it is/goes through me

 

Thanks for explaining.
Wouldn't it be more sensible to say that indeed the "equations do not relate to reality", rather then to assert that they do ?

 

Equations do represent reality. Some do not though.

We can safely say this.

The reason why is because we can measure reality as it unfolds to us.

I see no other reason to say that i exist if i can say ''I do.''

Reiku

 

Equations do not represent reality, only in a perfect world.

 

Remember though, there is no such thing as a perfect universe in a multiverse theory.
I find that our calculations (perhaps not so much string theory), represent quite a safe reality of understanding.
We have lots more to work out though, for sure. But yes. Equations represent reality. We have many of them, and we will conclude to create them, whether or not at the despense of ever finding a Grand Unification.

Reiku :m:

 

Only read post of this page, not all. hope not already noted, but tachyons not very likely to exist, but if they do they always travel faster than light. As they slow down to near light speed their mass tends to infinity. The neutrinos nevers goes faster than light. Neutrinos do exist. (Actually three different types, but they can convert type - final part of how the sun shines mystery was solved by realizing this conversion does occur.) Solar fusion is now a totally understood process, I am almost sure, with all testable predictions of the model now confirmed.

 

Sounds about right.

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articles to you for reference

1. A proposal to the neutrino as a tachyon is in arxiv.org/abs/hep-th/0011087

2. A theory of tachyons where the imaginary number is unnecessary arxiv.org/abs/0911.2359. All quantities are real.

3. Another hypothesis of the neutrino as a tardyon is arxiv.org/abs/0909.1856. Suppose the neutrino has a fixed speed regardless of the velocity of the observer and the source just like that of light speed in SR. Thus, the rest mass is zero and parity is broken. Three neutrinos have different velocities which behave as if oscillation. If the invariable speed is less than c but relativistic equations are applied to calculate the rest mass, the square is seemingly negative.