Bilge wrote:

Schoenfeld:

Bilge wrote:

Does that mean you want to know why that isn't consistent with
relativity or why it can't be true in nature? It's inconsistent
with relativity, because relativity precludes information from
propagating faster than `c'.

That's not necessarily true. Special Relativity does not strictly
forbid superluminal particles.

I'm not going to deal with this again. Relativity precludes
information from propagating faster than `c'.

That's right, and my statement is perfectly consistent with that.

The rest of what
you have below is irrelevant.

You are just unskilled to understand it.

The only purpose any of that serves
is to turn a clear and concise statement and obfuscate it.

It seems obfuscated to you, but it's basic stuff.

Would
you like to elaborate and show those things are irrelevant? I
didn't think so.

Sure.

-------------

1. Special Relativity prohibits ordinary particles (tardyons) from
accelerating past lightspeed.

[ELABORATION]
The relativistic energy of a body is given by:
E = gamma m0 c^2

where
gamma = 1 / sqrt(1 - v^2/c^2)

Since a tardyon is a particle characterized by time-like 4-momentum,
the velocity v of a tardyon is less than c. But as v approaches c,
gamma approaches infinity and thus statement (1) is true because
infinite energy is required to accelerate a tardyon to light speed and
beyond. However, this only applies to particles accelerating towards
lightspeed. It does not say anything about particles already existing
with superluminal velocities, which brings me to my second point.

--------------------

2. Special Relativity also prohibits superluminal particles (tachyons)
from decelerating below lightspeed.

[ELABORATION]

A tachyon is a particle characterized by space-like 4-momentum. Such
particles have superluminal velocities. For a tachyon to reach
lightspeed it thus needs to DECELERATE. But from the gamma relation, as
superluminal v approaches c then again, infinite energy is required. So
statement (2) is true.

--------------

3. If particles characterized by space-like 4-momenta and imaginary
proper-time make no observable interactions with time-like matter then
spacetime causal structure remains preserved.

[ELABORATION]

As you've learned, superluminal particles have space-like 4-momentum.

From the gamma relation,

gamma = 1 / sqrt(1 - v^2/c^2)

We see that gamma evaluates to a complex number when the velocity is
superluminal. Since the proper time of a particle is defined as
dTau = dt / gamma
we see then that superluminal particles have imaginary proper time
(hint: a complex number is imaginary).

The objection you raised was causation violation caused by superluminal
particles. Had you read properly, you would've seen I explicitly
covered this with
"If particles characterized by space-like 4-momenta and imaginary
proper-time ****make no observable interactions***** with time-like
matter then spacetime causal structure remains preserved".

This means quite simply that time-like matter interacts with time-like
matter, and space-like matter interacts with space-like matter. No
_observable interactions_ occur between them thus preserving spacetime
causality.

This brings me to my final point.

-------------

4. Superluminal particles arise in various theoretical contexts
including QFT/String theory where tachyon condensation potentially
account for the observed spontaneous violation of the electro-weak
symmetry.

[ELABORATION]
Someone who professes authority over physics (someone like you) should
know this, if you don't then you are a hack.

Special Relativity prohibits ordinary
particles (tardyons) from accelerating past lightspeed. Special
Relativity also prohibits superluminal particles (tachyons) from
decelerating below lightspeed. If particles characterized by space-like
4-momenta and imaginary proper-time make no observable interactions
with time-like matter then spacetime causal structure remains
preserved. Superluminal particles arise in various theoretical contexts
including QFT/String theory where tachyon condensation potentially
account for the observed spontaneous violation of the electro-weak
symmetry. Despite not violating any known physical laws, tachyons are
deemed unlikely by most physicists today.

Stop posting stuff that you know nothing about. Here's a description
of a tachyon from ``Quantun Fields and Strings: A Course for Mathemat-
icians,'' witten, et al. ``In classical physics a tachyon is a particle
which travels faster than light. Quantum mechanically, a tachyon would
be a particle of negative mass squared. However, tachyons never arise
as excitations of stable vacuums... An important example of a significant,
but not completely well-defined theory that has a tachyon is the bosonic
string theory. The bosonic string theory is not really well defined
because of the tachyon...''

Had you bothered to read what I said, I finished my statements with:
"Despite not violating any known physical laws, tachyons are deemed
unlikely by most physicists today."

Which relativistic theory do you think is well-defined and also
contains a tachyon?

Relativity does not strictly forbid tachyons, as I've explicitly shown
you.

Rather than professing authority over subjects you are clearly ignorant
on, why don't you at least bother to understand it?