The Great Phi Theory.

[SPOOFE]

I think what Bonzer is trying to say is this: “We know what the words mean. We know how to use them. Mr. Winter’s passage is the equivalent of saying ‘Bowling ball trampoline orange flexible left.’”

[sturmhauke]

No, SPOOFE, it’s “bowling ball trampoline tangerine malleable counter-clockwise”. This is a subtle yet important distinction.

[SPOOFE]

My apologies, Sturmhauke. I stand corrected.

[drewbert]

Yeah, but it should really be in ALL CAPS.

[Michael_Ellis]

:mad:

All your –

several hundred gunshots, plus a baker’s dozen 155mm artillery shells and a pair of daisy cutters.

…

mucho silencio

[robby]

[sub]<Monty Python>
I’m not dead, yet!
</Monty Python>

[Michael_Ellis]

All your Tug-Ahoy are belong to –

gunshot

…

silence

[Hiyruu]

First, I apologize to bonzer, I can see his point. Even though I don’t have the answers to the universe, I made this thread for the purpose of discussion, and contemplation on the topic, instead the topic has become confrontational, I apologize for this. When I make a post I will try to create dialog.

I have a question, that I hope someone can answer. I have cited the following theory on superluminal phenomenon, can someone explain how Phi is significant here:

http://www.weburbia.com/physics/tachyons.html

How about using tachyons to transmit information faster than the speed of light, in violation of Special Relativity? It’s worth noting that when one considers the relativistic quantum mechanics of tachyons, the question of whether they “really” go faster than the speed of light becomes much more touchy! In this framework, tachyons are waves that satisfy a wave equation. Let’s treat free tachyons of spin zero, for simplicity. We’ll set c = 1 to keep things less messy. The wavefunction of a single such tachyon can be expected to satisfy the usual equation for spin-zero particles, the Klein-Gordon equation:

            (BOX + m2)phi = 0

where BOX is the D’Alembertian, which in 3+1 dimensions is just

            BOX = (d/dt)2 - (d/dx)2 - (d/dy)2 - (d/dz)2.

The difference with tachyons is that m2 is negative, and m is imaginary.

To simplify the math a bit, let’s work in 1+1 dimensions, with co-ordinates x and t, so that

            BOX = (d/dt)2 - (d/dx)2

Everything we’ll say generalizes to the real-world 3+1-dimensional case. Now - regardless of m, any solution is a linear combination, or superposition, of solutions of the form

            phi(t,x) = exp(-iEt + ipx)

where E2 - p2 = m2. When m2 is negative there are two essentially different cases. Either |p| >= |E|, in which case E is real and we get solutions that look like waves whose crests move along at the rate |p|/|E| >= 1, i.e., no slower than the speed of light. Or |p| < |E|, in which case E is imaginary and we get solutions that look waves that amplify exponentially as time passes!

We can decide as we please whether or not we want to consider the second sort of solutions. They seem weird, but then the whole business is weird, after all.

1. If we do permit the second sort of solution, we can solve the Klein-Gordon equation with any reasonable initial data - that is, any reasonable values of phi and its first time derivative at t = 0. (For the precise definition of “reasonable,” consult your local mathematician.) This is typical of wave equations. And, also typical of wave equations, we can prove the following thing: If the solution phi and its time derivative are zero outside the interval [-L,L] when t = 0, they will be zero outside the interval [-L-|t|, L+|t|] at any time t. In other words, localized disturbances do not spread with speed faster than the speed of light! This seems to go against our notion that tachyons move faster than the speed of light, but it’s a mathematical fact, known as “unit propagation velocity”.

2. If we don’t permit the second sort of solution, we can’t solve the Klein-Gordon equation for all reasonable initial data, but only for initial data whose Fourier transforms vanish in the interval [-|m|,|m|]. By the Paley-Wiener theorem this has an odd consequence: it becomes impossible to solve the equation for initial data that vanish outside some interval [-L,L]! In other words, we can no longer “localize” our tachyon in any bounded region in the first place, so it becomes impossible to decide whether or not there is “unit propagation velocity” in the precise sense of part 1). Of course, the crests of the waves exp(-iEt + ipx) move faster than the speed of light, but these waves were never localized in the first place!

The bottom line is that you can’t use tachyons to send information faster than the speed of light from one place to another. Doing so would require creating a message encoded some way in a localized tachyon field, and sending it off at superluminal speed toward the intended receiver. But as we have seen you can’t have it both ways - localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal.

[SPOOFE]

As Troy McClure would say… “That’s not a question, professor.”

It starts with a flawed basis: “How about using tachyons to transmit information faster than the speed of light, in violation of Special Relativity?” It assumes that if data can be transmitted faster than light, that proves that the theory of general relativity is flawed. Hence, proof of the existence of tachyons would be evidence against relativity.

The problem is that relativity does allow for objects to travel faster than light. It would simply require more-than-infinite energy for an object with mass to do so.

A simple Google search for “Tachyons” revealed a few sites:

From this site:

While many believe that the existence of particles with hyperluminal (superluminal) velocities (FTL, or Faster-Than-Light velocities) is precluded by relativity, this is not the case if the particle is created with a velocity already exceeding the velocity of light. What relativity precludes, within the boundaries of our present technologies, is the acceleration of a subluminal particle to hyperluminal velocities.

It basically says that the object travelling FTL is still not travelling AT the speed of light, which, as relativity tells us, would require infinite energy. It also espouses the “negative mass” theory for tachyons.

Further, from this site:

Now another familiar relativistic equation is E = m*[1-(v/c)2][sup]-1/2[/sup]. Tachyons (if they exist) have v > c. This means that E is imaginary! Well, what if we take the rest mass m, and take it to be imaginary? Then E is negative real, and E^2 - p^2 = m^2 < 0. Or, p^2 - E^2 = M^2, where M is real. This is a hyperbola with branches in the spacelike region of spacetime. The energy and momentum of a tachyon must satisfy this relation.

You can now deduce many interesting properties of tachyons. For example, they accelerate (p goes up) if they lose energy (E goes down). Furthermore, a zero-energy tachyon is “transcendent,” or infinitely fast.

This states that the speed of light - C - is still the “Holy Grail” for both sides of the spectrum, i.e. it would require infinite energy to get an object with positive mass to accelerate to C, and it would require infinite energy to get an object with negative mas to decelerate to C. Further, just as an object with positive mass would be completely at rest if it had zero energy, an object with negative mass would travel at “infinite speed” if it had zero energy (Warp 10?).

Again, it’s just a theory, but I post this to remind you that your little PHI pet isn’t the only possible explanation for seemingly “contradictory” evidence.

[SPOOFE]

Oop, forgot to add this (I was too busy laughing at a Conan O’Brien joke)…

Note that your cite and mine use the same equations. They use similar descriptions of those equations. But further note that your cite seems insistent on throwing “PHI” into the works without trying to explain why it is necessary. And also note the flawed premise.

[TwistofFate]

When I make a post I will try to create dialog

Which is a good thing, but how about trying to finish some of the other dialogue that is in the thread?

you have been asked questions, but you havent answered them.
Aned remember, answering them also involves explaining your answers.

[Truth_Seeker]

*Originally posted by Hiyruu *
**
I have a question, that I hope someone can answer. I have cited the following theory on superluminal phenomenon, can someone explain how Phi is significant here:

http://www.weburbia.com/physics/tachyons.html

**
[/QUOTE]

This would be hysterical if it weren’t so bloody sad. You want someone else to exlain how “superluminal phenomenon” (which, FTR have never been observed) relate to your theory of Phi? If there is one thing that even you would agree on after the last FIVE PAGES of this thread, it’s that NO ONE besides you claims to have any idea what you’re talking about. It is also painfully obvious that even you don’t know what you’re talking about because your theory isn’t a theory. It predicts nothing, is full of undefined terms and, what is worse, actually fails to predict the known data, e.g. regarding gravity. The Great Phi Theory is as a tale told by an idiot, full of sound and fury, signifying nothing.

For what it’s worth, the “Phi” in the Klein-Gordon equation is roughly equivalent to Psi, the wave function. Phi is traditonally used instead of Psi in the KG equation because solutions to the KG can’t be interpreted as probability densities. If you really want the details, I’d refer you to

http://www.pact.cpes.sussex.ac.uk/users/markh/RQF1/node15.html

H. is either a troll or completely impervious to logic. In either case, this thread should be allowed to die. Let H. post to himself, if he wants to. If you must post to this thread, I recommend posting ONLY smilies. I have no doubt you can make a more coherent argument with them than you can with the Great Phi Theory.

[Satyagraha]

But, Truth Seeker, ALL OF LIFE is a “tale told by an Idiot, full of sound and fury, signifying nothing.” How can we pick on H. when Dubya is in the White House???

[bonzer]

*Originally posted by Hiyruu *
First, I apologize to bonzer… I have cited the following theory on superluminal phenomenon, can someone explain how Phi is significant here:

Apology accepted.
Actually, the page you’re citing here is sensible physics. I realise that to someone who isn’t very familiar with physics or mathematics and how they work, it may look like what Dan Winter writes. But it’s intended to be explicitly hypothetical - the author isn’t claiming that tachyons actually exist. (In the fourth paragraph they explicitly say “if they exist” about them). It describes how tachyons would behave, based on the known laws of physics, if tachyons were found to exist. However, no professional physicist believes that there is evidence that they exist, as the author of that page would probably be the first to admit. Again, I realise that if you don’t know what’s already well established physics, it may be difficult to tell what’s the firm stuff and what’s the small amount of (fun) speculation.

I hate to break it to you, but the references to “Phi” here are entirely arbitrary. It’s just a name. They could have called this field “Alpha”, “Beta”, “Bob” or “the Klein-Gordon field”. It’s nothing to do with spirals or the Golden Ratio - it’s just that there are only 20-something or so Greek letters and hence physicists and mathematicians have to reuse them in different contexts. They’d prefer not to, but that’s the way it is.

Just because a well-known scientist/philosopher and a well-known painter have the same surname (Francis Bacon), it doesn’t mean they’re the same person. But if you know little about either subject, it can get confusing. Superficially, it’s the same person, but they’re actually not.

Sorry, no smilies

[Truth_Seeker]

;j

[Hiyruu]

SPOOF, I will try and find a definition of what that equation is for.

It is called the ‘Klein-Gordon equation’:

(BOX + m2)phi = 0

Definition: http://thunder.prohosting.com/~siltec/wwwboard/messages/25.html

Mechanical interpretation of the Klein-Gordon equation

The substratum for physics can be seen microscopically as an ideal fluid pierced in all directions by the straight vortex filaments. Small disturbances of an isolated filament are considered. The Klein-Gordon equation without mass corresponds to elastic stretching of the filament. The wave function has the meaning of the curve’s position vector. The mass part of the Klein-Gordon equation describes the rotation of the helical curve about the screw axis due to the hydrodynamic self-induction of the bent vortex filament.

[Truth_Seeker]

:rolleyes:

[SPOOFE]

SPOOF, I will try and find a definition of what that equation is for.

I will try to say this as politely and as kindly as is possible for me to muster in response to such a statement.

::deep breath::

I NEVER ASKED FOR A FUCKING DEFINITION OF THE EQUATION.

You said you wanted to start a dialogue. Good. Now, prove that you are NOT a liar and go back in this thread and answer the other questions - see, participate in a dialogue - that have been posed to you.

[Meta]

Particles ain’t particles, except the proton.

Meta

[scotth]

Revived after a year and two days dead.

Other than that complaint, you are completely wrong Meta.