Bill Nye I'm not .

Tachyons are a hypothetical concept, that may not exist, therefore an unknown quanitity that could explioted in a fictional story.

If tachyons do exist, according to the current understanding of relativty, they would always travel faster then light.

I find it difficult to see how tachyons could interact with a craft, much less propel subluminal mass over the speed of light.

Do they go right through things? Unknown, since we have no idea if they exist. It would sound reasonable they would not interact with normal matter.

Maybe you had in mind neutrinos (a sub-luminal particle, uncharged, with a very low mass, and only weakly interacting). The sun produces streams of them from nuclear reactions and millions are passing through us each second. I think I read somewhere long ago they could pass through 7 lightyears of lead without interacting via the weak nuclear force.

Of course, neutrinos travel slower then light, though quiet close to it, and like anything else are effected by gravity.

Gravity is nothing more than objects moving in the straightest possible path through curved space-time. Tachyons would move through space-time and thus be effected as well.

Of course, anything moving faster then light would, at least the math says, travel backwards in time. If time is anything other than a rate of change, perhaps this would have meaning. But even traveling backwards in time, it would be effected by the curvacture of space-time.

Would they be constant, like the jet stream or the solar wind? Like you indicated it would depend on the source. Likely tachyons would always be tachyons from thier creation, and subluminal would always be subluminal. The speed of light would be a great wall which niether could cross.

If you don't research this well, your readers might never buy it. In order to write a credible SF story, it looks like it would help to pick up a book or two on relativity.

Of course, you might not need to have a tachyon mechanism to explain your FTL, not to have a good story.

If you do it, know enough about what modern theory thinks is possible and be sure to be consistent with the physics you assign to your invented particles.

First, there is quantum technology right now that is FTL.
But it doesnt accelerate mass. In fact it cant. What it can
do is carry information and that's just as important if you
want to get someplace else in the universe.

The second is also a quantum discovery that has been demonstrated.
That's teleportation. Yup, one atom in a single state has been
teleported to another atom someplace else.

Combine those two ideas and you have a transporter like the
one in... well, you know :-)

As for the behavior of tachyons, I can tell you what I've learned so far, half-way through my relativity course. My thinking is that they WOULD be affected by gravity, but not like you'd think. Here's my reasoning (helped along by the qualitative stuff I've heard about tachyons + a few google searches).

The energy relation is E^2 = p^2c^2 + m^2c^4. You'll notice that for mass at rest (p=0) the popular E=mc^2 pops out.

For massless particles, E=pc, and they can't move faster than light. Period.

BUT if you throw in a rest mass: E=mc^2 where m is the relativistic mass, m=gamma*m0 where m0 is the rest mass and gamma = sqrt(1 - (v/c)^2). The important bit here is that square root. It says that if v > c, your energy is imaginary. Which is silly. SO, why not make your mass imaginary? i*i= -1, which means E < 0.

Now it gets interesting. Negative energy. {twitters fingers spookily} Let's look at the component of energy due to momentum: E=pc. If E < 0 then when you increase momentum, the tachyon has less energy. This is the big weird thing you'd read about if you did any search on tachyons. It implies something for nothing and is well...weird. (Also, I think that gravity would be a repelling force.)

I'm not sure what general relativity has to say on the subject, so I can't be of any help there. All this stuff holds true for constant speeds though.

EDIT: Oh, a note on the path tachyons take. That falls out of some equation df/dx - d^2f/dtdx'=0 where f is a path function for some integral with Euler's name in it...don't have my notes with me now. But the point is that f = kinetic energy - potential energy and this differential is satisfied when f is minimized--basically, all the force equations (and, hence, equations of motion) you were ever given in classical physics fall out beautifully. My thinking is that if f < 0, the path would be nothing like you would get from ordinary matter.

I know we have some physicists here who know far more about this whole thing than I--anyone care to comment??

Seems like tachyons were once a viable theory, but have since become more of a fiction. I don't know enough to understand just how thoroughly they've been debunked, but I get the idea it's not popularly believed anymore.

That negative energy stuff looks good though.

It ties back to the wave/particle mystery. Unfortunately, for the last 50 years or so, physicists have been under the Copenhagen mindset, which basically ignores trying to find underlying causes of the mystery and just concentrate on effects.

No one has knocked down Copenhagen yet, and many have tried. For
all the trying it gets _stronger_. I'd tend to stand with it.

I readily admit to my ignorance on this, it's a very difficult, deep, and non-intuitive subject. I would love if somebody would explain Bell's Inequality to me, and how it proves nonlocality. I have yet to read a laymen's explanation that didn't make my eyes blur.

Someone correct me if I'm wrong, I'm getting in over my head. Quantum entanglement and 'teleportation' are just another manifisation of the quantum waveform. Entangled particles become part of the same waveform and assume multiple states, until the waveform collapses, and the particles assume one state or the other.

For instance, an EPR varation: A particle with zero angular momentum decays into two lighter particles that fly off in opposite directions. They are entangled and part of the same wave function. If an outside agency measures one of the particles, they would find the angular momentum either a plus or minus and thus could assume that the other particle has the opposite quanity. However, before that measurement, both particles were in a superposition of states, that is BOTH plus and minus at the same time. When one of the particles is measured, the waveform collaspes (the superposition goes away) and the particle assumes one state or the other. It's partner will instantaneosly assume the opposite state. This will happen instantaneosly if the particles are a nanometer apart or a billion lightyears apart.

However, it is my understanding, that the measurer cannot control which state the particle will assume, nor can they predict it. They can only assign a probiblity of the particle having that state. Therefore a signal could not be constructed using that method. Or at least, that's what I've heard.

And assuming it could (and let's hope it turns out we can) and let's say we want to use QT to send a signal to the Centari system, 4 lightyears away. Particles would have to be entangled first. One set of particles would already have to be Centari, having to travel 4 lightyears to get there.

Signal noise is due to complexity. Each blip in the signal could be predicted if given all the factors to calculated. Of course, if we could do that, we could predict the weather.

The problem with using QT to communicate FTL goes deeper then that, it is part of the inheriant uncertainty that is a principle of the quantum world.

(Forgive my spelling...)

Bell's Inequality, as I understand it: Certain quantities, according to QM, cannot be mutually known. Momentum and position, energy and time, so on. But if you entangle two particles (they are, in the wave sense, the same particle--they are described by one equation) you should be able to measure one quantity of one, and thus know the other quantity of the other. Spin is what the experiments have tested, yeah? Anyhoo, QM says this is a no-no, but Bell said, there's a way we can test it. (Wasn't Einstein involved in this too? He hated QM...)

Locality means that nothing travels faster than light. If Bell's Inequality holds, it suggests nonlocality because when you plug all your measurement into the inequality, it's true only when you only know as much about the system than QM says you can. (The fact that you measured one property of one particle travels instantaneously to the other and changes it.)

If you could measure each property, then that means the information is contained separately in each particle (they aren't really the same wave, so to speak). No locality violation.

Don't ask me WHAT the inequality is, or how the experiments worked. It sounds like a huge engineering challenge to actually simultaneously measure entangled particles.

Bell's Inequality:

Introduction, We know there is observable stuff about particles
like locality in space. Our friend apeiron showed us that velocity
'v' and momentum 'm' are determinable things.

Weird Quantum Part, There would be systems in the universe that
are interrelated such that when one part is observed separately
it will determine the corresponding measurement of the second part.
(Think photons) What is measured is "spin". This is not something
politicians use, or even something a top does. In fact we could
just as easily assign names like "up" and "down" to what our spinning
does, and so we do because we are clever.

How do we as scientists and engineers reconcile such strange stuff?

a) Accept that quantum things happen, and avoid reading or discussing
special relativity.

b) Decide that quantum mechanics is incomplete and there something
we are missing.

If you are Einstein and his pals you pick b) mostly because you authored
special relativity. It's considered the greatest accomplishment of the
20th century and it would be really embarrassing if it were wrong.

Weasel Part, You make up something called "hidden variables". The
hidden variables do something very simple, they commute the characteristics
of the first photon to the second in some as yet unknown way so that
each part interacts. Action from a distance is a parlor trick.

Note:

This is why I drew the analogy yesterday to the flatlander and the pencil
If the poor guy could just realize that his space had been folded
and the pencil was really the same pencil poked through in two places
everything would be fine. But I digress...

John Bell came up with a method to test for those hidden variables.
He showed that if his inequality was satisfied there could be
hidden variables.

It's pretty simple: you get six states. It is easier to comprehend
if you give some simple assignments to them A+ A- B+ B- C+ C-

These are things we can measure about photons and they obey these rules.
Because it wouldn't be a fun game if there weren't rules

The Rules. Where N is "The number of" function

1) N(A+ B+) = N(A+ B+ C+) + N(A+ B+ C-)

2) Every photon has a unique state when measured (You cant
measure both the A and the B of a photon)

There are corollaries and stuff if your interested, but I think you get
the idea.

Inequality Part,

So every (Ai Bj C+) (Ai Bj C-) is just (Ai Bj) should be clear...

Let n[A+ B+] designate every photon pairs where the first photon
measured A+ and the second measured B+. Follow the same schematic
for the other pairs.

Big fat truth:
N[A+ B+] <= N[A+ ? C+] + N[? B+ C-] or...

If there is some other state out there 'X' then the inequality will hold

Tomorrow can I tell my story about FTL communications, and
teleportation? Please? Please?

[This message has been edited by john d. clark (edited November 09, 2005).]

(Without reading the posts between his and this one)

That is an interesting analysis. It brings to mind dark energy, which you probably know, has now brought the expanding universe and negative gravity into vogue. The negative energy of the Aperion Tachyon seems to fit quite well into that science at first glance.

j.d. clark: Isn't that all just a wordy version of the Pauli Exclusion Principle?

So, uhm spaceman "dark energy" is simply a way to fill in the rate of expansion of the universe with some unknown value so the equations will fit. Think I am pumping up
a tire at x psi but its expanding at x+y. It's another way to sound cool when you dont know whats really happening.

One more dirty little secret a black hole cant form. Not under general relativity. It's time line should go asymptotic before it can collapse

[This message has been edited by john d. clark (edited November 10, 2005).]

Ok, I went back to general relativity.

Try http://www.phy.mtu.edu/bht/bh_pub_faq.html

3. Won't it take forever for you to fall in? Won't it take forever for the black hole to even form?

It's pretty clear if you are the "observer" it wont. I really like the phrase " Not in any useful sense." and "if I somehow stood on the surface of the star as it became a black hole, I would experience the star's demise in a finite time." Yeah, that's useful, and it could happen.

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j.d. clark: Isn't that all just a wordy version of the Pauli Exclusion Principle?

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Spaceman, no it isnt the same.

Try http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html

This does a better job then I ever could here. FYI the spin discussed here inst electron spin, and it's not angular momentum. Heck, photons are massless.

[This message has been edited by john d. clark (edited November 09, 2005).]

[This message has been edited by john d. clark (edited November 11, 2005).]

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Aperion
(Without reading the posts between his and this one)

That is an interesting analysis. It brings to mind dark energy, which you probably know, has now brought the expanding universe and negative gravity into vogue. The negative energy of the Aperion Tachyon seems to fit quite well into that science at first glance.

j.d. clark: Isn't that all just a wordy version of the Pauli Exclusion Principle?

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First things first: it's 'her.'

Yeah, that's the first thing I thought too. I know nobody attributes tachyons to the expanding universe (why would require a more thorough look at tachyons that I don't have the background to give), but anything with negative energy will have those properties. Strange stuff. Though, speaking off the cuff, I don't like dark energy one bit. Sort of what john said:

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So, uhm spaceman "dark energy" is simply a way to fill in the rate of expansion of the universe with some unknown value so the equations will fit.

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Let me explain. I know the cosmological constant can fall purely from Einstein's analysis, but its value, purely mathematically speaking, should be dependent on initial conditions of the universe. (If you've had calculus, it's that constant you get when performing and indefinite integral.) But relativity is incomplete and cannot account for the IC's. So it is very true to say that the cosmological constant is NOT accounted for by known theory. Right now it's being used as a fudge factor.

Don't get me wrong, there have been some very famous fudge factors. Planck's constant comes immediately to mind. But so does Vulcan. Few people know about Vulcan, but before Einstein said otherwise, there was a widely supported theory to explain the inability of Newtonian gravity to account for the orbit of Mercury that said there was another planet dubbed Vulcan even closer to the sun. People tried to deduce its mass and orbit even.

It's a tricky thing making predictions. Newton predicted Vulcan and got it wrong. Einstein predicted black holes--and even he didn't believe in them, I don't think--but there you go. (By the way, I've never heard that general relativity doesn't account for black holes. Care to go into more detail?)

As for Pauli's Exclusion Principle, I don't see the connection (photons are bosons after all), could you explain?

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apeiron, dont at least you want to take a crack at shooting down Bell's inequality. Doesn't the proof look kind of flimsy? Think timing between measurements. How do we really know the photons are measured at the same time.

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And another thing I am not evn a person I am just a cocker spaniel
at a computer terminal someplace. My master is out splitting atoms
someplace and I just sort of have the run of the house. You dont believe
me? Just check out http://www.dsldog.com

[This message has been edited by john d. clark (edited November 10, 2005).]

I edited the post about Bell's inequality to. I got confused and
thought the inequality implied that QM was valid. Later I looked
at the proof and realized I was wrong. I am so ashamed...

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First things first: it's 'her.'

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Incidentally I was looking at one of the Pauli equations:

w = w1(a) w2(b) +- w1(b) w2(a)

The wavefunction for the state in which both states "a" and "b"
are occupied by the electrons can be written. I see that +- IS required for
Bosons and fermions. Apeiron, does Spaceman have a point that Pauli
equations apply to photons?

[This message has been edited by john d. clark (edited November 11, 2005).]

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Are you refering to how as the star collapses, time slows so that it would take an infinite amount of time (from an outside observer's view) to form?

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Chris, yes I am. I have edited the post to point you someplace you can read more about it. This sort of thing should surprise nobody as apeiron said, general relativity is incomplete. Heck, mathematics herself isnt even up to the task of fully describing mathematics :-)

[This message has been edited by john d. clark (edited November 11, 2005).]

And yes, I suppose we digital folk DO look an aweful lot alike. Though I fancy my smilies have a few more eye lashes.

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and your mistaking electrons for bosons to. We must get you some help.

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