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## Main Question or Discussion Point

A tachyon is a hypothesized particle that has imaginary mass (imaginary numbers) and moves faster than light speed. I don't believe in it because it can't have imaginary mass, what about you?

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A tachyon is a hypothesized particle that has imaginary mass (imaginary numbers) and moves faster than light speed. I don't believe in it because it can't have imaginary mass, what about you?

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JesseM

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It's not good practice to dismiss possibilities based on thinking the math is too "weird"--do you also object to the use of wavefunctions in quantum mechanics, which can have complex (real + imaginary) amplitudes? A more physical reason to object to tachyons is that according to relativity any particle that would allow for FTL signal transmission would also allow signals to be transmitted backwards in time (see here), and there are also some more complicated arguments against them from quantum field theory discussed here. Aside from these theoretical objections, there is also the fact that no empirical evidence has been found to support their existence!A tachyon is a hypothesized particle that has imaginary mass (imaginary numbers) and moves faster than light speed. I don't believe in it because it can't have imaginary mass, what about you?

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K^2

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As far as I can tell, the only real problem with Tachyons is that a particle traveling faster than light has no means of interacting with ordinary matter or with light. So suppose there are some. We cannot interact with them in any way. Then does it matter if they exist or not? No description of what we observe can every include them.

The only loophole I can see is if they interact with matter under event horizon, which might allow the interaction to leak when a quantum black hole evaporates away. But this is way too many "if"s.

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but imaginary mass means like how do its particles look like? if the tachyon itself is the particle, how much matter does it have? imaginary is the answer. means the particle itself is imaginary?It's not good practice to dismiss possibilities based on thinking the math is too "weird"--do you also object to the use of wavefunctions in quantum mechanics, which can have complex (real + imaginary) amplitudes? A more physical reason to object to tachyons is that according to relativity any particle that would allow for FTL signal transmission would also allow signals to be transmitted backwards in time (see here), and there are also some more complicated arguments against them from quantum field theory discussed here. Aside from these theoretical objections, there is also the fact that no empirical evidence has been found to support their existence!

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Vanadium 50

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Read the message above. If they don't interact with light at all, what does that tell you about what they look like?but imaginary mass means like how do its particles look like?

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HallsofIvy

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Essentially, you are saying, "I do not understand this, therefore it cannot be true." That's not a valid argument!but imaginary mass means like how do its particles look like? if the tachyon itself is the particle, how much matter does it have? imaginary is the answer. means the particle itself is imaginary?

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JesseM

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What does the mass have to do with what the particle "looks like"? A photon has zero mass, do you think that means the photon doesn't exist? Mass is just a mathematical quantity associated with the particle that helps determine how it behaves, not fundamentally different from, say, charge (which can be positive or zero or negative--do you think negative charge "means the particle itself is negative"?)but imaginary mass means like how do its particles look like? if the tachyon itself is the particle, how much matter does it have? imaginary is the answer. means the particle itself is imaginary?

Also, please don't attach too much significance to the label "imaginary", it's just an arbitrary label mathematicians came up with for the square root of a negative number, it has nothing to do with the ordinary English sense of the word "imaginary" as unreal or existing only in the mind.

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Having imaginary mass? Going faster than light? It cannot have imaginary mass so they probably do not exist.

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JesseM

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There are no basic principles of physics that rule out imaginary mass. Don't take the word "imaginary" too literally, it's just a technical term that has no real connection with its English meaning; as I mentioned earlier, imaginary numbers already have an important place in physics in the sense that the amplitude of the quantum wavefunction is in general a sum of an imaginary number and a real number.Having imaginary mass? Going faster than light? It cannot have imaginary mass so they probably do not exist.

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Well I do now. Imaginary mass=i

imaginary speed=i

Kinetic Energy=(iˆ2)ˆ2

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JesseM

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A tachyon would not have imaginary speed, it would have a real speed, larger than c. For a massive particle, the total energy (rest mass energy + kinetic energy) is given by E=gamma*mc^2, with gamma = [tex]\frac{1}{\sqrt{1 - v^2/c^2}}[/tex]. For v > c, gamma is imaginary, so if the rest mass m is imaginary as well, E will be a real number.Well I do now. Imaginary mass=i

imaginary speed=i

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OK, now, I've started to think that tachyons are true,,, though they are used to paradox theories (like the bosonic string theory)What does the mass have to do with what the particle "looks like"? A photon has zero mass, do you think that means the photon doesn't exist? Mass is just a mathematical quantity associated with the particle that helps determine how it behaves, not fundamentally different from, say, charge (which can be positive or zero or negative--do you think negative charge "means the particle itself is negative"?)

Also, please don't attach too much significance to the label "imaginary", it's just an arbitrary label mathematicians came up with for the square root of a negative number, it has nothing to do with the ordinary English sense of the word "imaginary" as unreal or existing only in the mind.

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I think that if the tachyon deccelerates to c, it should need infinite enrgy and if energy approaches 0, its speed increases to infinite. I guess these tachyons could be wrong, or probably theres a tachyon constant which a tachyon's speed would be at 0 energy.

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JesseM

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Well, like I said there are some other reasons to be highly skeptical that they actually exist in the real world, like the fact that according to relativity any ability to send faster-than-light signals would also allow you to send signals backwards in time and violate causality. I was just saying that pointing to the imaginary mass of tachyons is not a very good argument for ruling them out, but there are better arguments for thinking they don't exist.OK, now, I've started to think that tachyons are true,,, though they are used to paradox theories (like the bosonic string theory)

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Matterwave

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FTL signal propagation in Special relativity implies that one can construct an inertial, valid, frame of reference in which a effect can occur before a cause. If we want to maintain causality, the principle of relativity, and the constancy of the speed of light, do we not have to object to the concept of FTL travel? As far as I know, these three postulates have never been observed to be false in any experiment we have conducted to date.

Moreover, wouldn't tachyons have space-time intervals (S) which are space-like and therefore they cannot be localized to the same point in any frame of reference? (Can we, then, still call them particles?)

Doesn't this, at least sort of, imply that SR negates the possibility of Tachyons (tachyons as defined as particles which travel faster than the speed of light)?

There are no observable quantities in physics that I am aware of that returns an imaginary value. All observables, even in Quantum Mechanics, are real. Wave-functions are NOT observables, and moreover the probability density is the absolute square of the wave-function, which is REAL. In fact, this is a postulate of Quantum Mechanics. That observables must be represented by Hermitian operators guarantees that the eigenvalues (measurements) are real. If tachyons exist, wouldn't their "invariant mass operator" be non-hermitian and therefore violate this postulate of QM?

So, it would seem to me, that under the standard umbrella of physics, tachyons should not exist. If we do find tachyons in the future, I think we would have to modify some of the basic postulates of physics.

Of course, there is no reason the postulates of physics must be correct. After all, it is a basic principle of physics that empirical testing can only "support" (and not prove) any postulate of physics. But what I'm saying is, why give the thread starter a hard time about this?

Keep in mind that I do not pretend to be all-knowing about physics. My only point in this post is that there are lots of reasons why tachyons existing would be counter-intuitive even (perhaps especially) to someone who has studied physics.

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DrGreg

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Matterwave, as you've indicated, there are lots of good reasons for suspecting that tachyons don't exist, but imaginary mass isn't a particularly good one. In the mathematics of relativity, distance is effectively "imaginary time", but that doesn't cause us a problem because we work with real distance instead of imaginary time. Similarly we could come up with a new name for "imaginary mass" and use that as a real quantity defined for particles whose 4-momentum is spacelike rather than timelike.

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Matterwave

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I don't think I've ever heard the "distance is imaginary time" argument, can you clarify?

I know that because the metric tensor is diag(1,-1,-1,-1), there is a relative minus sign in the interval between the time coordinate and the space coordinates, and this is sometimes put into the 4-vector displacements themselves by adding an i in front of either the time-coordinate or the space-coordinate, but this seems unnecessary once one introduces the metric tensor.

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JesseM

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The metric line element for proper time (which could be integrated along a timelike worldline to get total proper time) is [tex]d\tau = \sqrt{dt^2 - (1/c^2)(dx^2 + dy^2 + dz^2)}[/tex], so if you pick a spacelike interval this gives an imaginary value for the proper time.I don't think I've ever heard the "distance is imaginary time" argument, can you clarify?

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Matterwave

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But since, space-like separated interval cannot be the path of any particle, the proper time, in that context, is not measurable, isn't it? Doesn't this argument just make one more problem with having tachyons (they would measure imaginary proper time in "their" frame)?

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Would this also imply that they would emit negaitive gravity?

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