
Why nothing can go faster than the speed of light - danteembermage
http://www.reddit.com/r/askscience/comments/fjwkh/why_exactly_can_nothing_go_faster_than_the_speed/
======
chime
For those not familiar with RobotRollCall (the author of the linked comment)
check out his profile and other answers. He is one of the best contributors to
AskScience and can explain almost any theoretical physics topic in
understandable terms. People joke that he is actually Neil deGrasse Tyson and
that he should really get this own column / talk show.

~~~
jimmyjim
_She_ is one of the best contributors to AskScience

~~~
nandemo
Meta-comment: I often see the above pattern on HN. Someone writes a very
informative comment with a minor inaccuracy. Someone replies to it only to
correct that inaccuracy. The reply then gets way more upvotes than the
original comment.

I don't particularly care about "karma", so what bothers me is not that the
original commenter didn't get enough points, but rather what people in the
community think it's important in a conversation.

~~~
shin_lao
This is called anal-retentiveness and is very frequent amongst geeks. Just
ignore it.

<http://en.wikipedia.org/wiki/Anal_retentive>

~~~
jimfl
Actually, it is called pedantry.

~~~
generalk
There's a joke there somewhere.

~~~
jberryman
Wait... this whole thread wasn't a running meta-gag?

------
jazzychad
I found that the author gave a great setup for an explanation, and then balked
at giving the actual answer.

> For right now, if you just believe that four-velocities can never stretch or
> shrink because _that's just the way it is_

In other words, nothing can go faster than the speed of light because that's
the way it is? The author needs to explain why the magnitude of this four-
velocity vector is the speed of light! I was hooked after the first few
paragraphs, but then felt like it dead-ended in a circular argument.

~~~
kalvin
She wrote several followup answers in the comments thread, one of which
addresses your question (though it might not be satisfying!):
[http://www.reddit.com/r/askscience/comments/fjwkh/why_exactl...](http://www.reddit.com/r/askscience/comments/fjwkh/why_exactly_can_nothing_go_faster_than_the_speed/c1gi47a)

Someone else wrote my favorite answer: "Basically, the way to think of it is
not that light is the fastest thing, but rather that there is a speed, c,
which the geometry of space and time demands is the fastest possible speed.

One can also work out that anything without mass must travel at this fastest
possible speed c. Light is one of those things, therefore light travels at c.
It's only an accident of history that we call c "the speed of light": that's
the context we discovered c's existence in.

As for why it's the speed it is, well, it's the speed in our universe. It's
actually much more natural to say c=1 and all speeds are then unitless numbers
between 0 and 1. From this point of view c is 300 Mm/s because of how we chose
to define the meter and the second."
[http://www.reddit.com/r/askscience/comments/fjwkh/why_exactl...](http://www.reddit.com/r/askscience/comments/fjwkh/why_exactly_can_nothing_go_faster_than_the_speed/c1gi276)

~~~
scorpion032
As of today, meter is defined in terms of the speed of light. We have come a
full circle!

> The meter is the length of the path travelled by light in vacuum during a
> time interval of 1/299 792 458 of a second.

via: <http://physics.nist.gov/cuu/Units/meter.html>

~~~
beza1e1
So how long is a second?

~~~
a1k0n
via Wikipedia: The duration of 9,192,631,770 periods of the radiation
corresponding to the transition between the two hyperfine levels of the ground
state of the cesium 133 atom.

So I guess that means a meter is 30.66331898849836976219 cesium-133 transition
periods.

------
coderdude
It's a shame that about 30% of the comments in this thread are about how the
author of the Reddit comment is female. I have a feeling the discussion on
Reddit actually trumps the discussion on HN for this one. What's worse is that
you have to wade through this irrelevance to get to the "good" comments on
here.

------
Stormbringer
People keep asking this, and similar things like "if you were travelling in a
vehicle at the speed of light and you turned on the headlights, what would
happen?"

For me the easiest answer is to understand that from the point of view of the
person travelling _near_ the speed of light the beam of light moves away from
them at the speed of light. So after ~1 second they are 300,000Km apart.

On the other hand, from the point of view of a 'stationary' observer, the
light and the spaceship emitting it are moving at almost exactly the same
speed. So after ~1 second they are maybe 1 meter apart.

How can this be? Our minds naturally want to reject this as nonsense. But the
thing the gripping hand is holding that makes this true is that to the
stationary observer and the person travelling near the speed of light time is
moving at different rates.

The person who is moving ~1m slower than the speed of light is experiencing
time enormously much slower than the person 'standing still'. The time
difference is 300,000,000 times (sic).

Our brains reject this, because we think of time as an absolute rock solid
constant, when in fact even with our primitive understanding and slow speeds
we can demonstrate experimentally that time is in fact flexible, and it _does_
slow down the faster you get.

~~~
Kilimanjaro
Say you just flick the lights on and off quickly just to let one photon
escape. Where will that photon be in reality in one second? 300kkm apart from
the rocket? one meter apart?

~~~
tel
The part that makes this so hard to grasp is that this question is ill-posed.
The "in reality" part is nonsensical.

A primary insight to general relativity is that it makes no sense to define
location (or motion) except relative to an observer. This means there's no
"true" position or motion, simply an infinite set of equivalently meaningful
but disagreeing ways to observe them.

(For interest's sake, acceleration is the lowest order local phenomenon. An
object does not need an external observer to measure it's own acceleration due
to the appearance of locally measurable "forces".)

So the answer is to excise "in reality" and then state that both answers are
equally meaningful and correct.

~~~
Kilimanjaro
When I say 'in reality' I mean physically. Say the rocket earthbound and is
2x300kkm from the earth, the question again, will the photon collide with the
earth or still be 300kkm from it?

The problem I have with light as a unit of reference is that 'perception' is
not the same as 'reality' in the physical world.

~~~
T-hawk
Relativity demands and demonstrates that there is no such thing as "'reality'
in the physical world". Events only occur and exist in the context of an
observer.

From the perspective of an Earthbound observer, the photon emitted by the ship
will travel from 600kkm away to 300kkm away in one second. (Actually the
observer cannot see the photon until another second elapses and it collides
with him on Earth.) This observer will see the ship and the photon moving
almost together, the ship slower by whatever infinitesimal fraction of c.

From the perspective of a shipborne observer, the photon emitted by the ship
will travel from 0 kkm (away from the ship) to 300kkm away also in one second.
How do we reconcile this with the knowledge that the Earthborne observer sees
the ship and the photon staying together? Length contracts in the direction of
travel. So the shipborne observer's meters are very short. The small distance
perceived by the Earthbound observer is perceived as a 300kkm distance by the
shipborne observer. <http://en.wikipedia.org/wiki/Length_contraction>

In general, this is how you resolve paradoxes in relativity: work it out from
the perspective of each observer and understand that there is no central
objective reality. You will find that you made an assumption that does not
hold true across both observers.

<http://en.wikipedia.org/wiki/Ladder_paradox>

If you can wrap your mind around the Ladder Paradox, you're well on your way
to understanding space-time transformations in relativity. The key to the
ladder paradox is that there is no such thing as an objective standard of
"simultaneous". Simultaneity is specific to each observer; two observers
perceive the simultaneity of two events differently.

------
ck2
Once you understand that, then read about (what I think is super-cool) : frame
dragging.

<http://en.wikipedia.org/wiki/Frame-dragging>

It causes satellites around earth to move a few feet each year.

~~~
lurker19
As I read the Wikipedia article, the frame dragging effect is hypothesized and
has not yet been observed, though experiments have been designed and some are
in progress.

~~~
ck2
They put two dummy satellites in orbit and measured the effect.

Tried to find a better source but this will do for now:

[http://articles.cnn.com/2004-10-20/tech/warped.space_1_black...](http://articles.cnn.com/2004-10-20/tech/warped.space_1_black-
hole-lageos-frame)

------
aufreak3
Here is what seems like a reasonable "explanation" to me -

\-- We figured out a few things about electric and magnetic fields. In
particular, a changing electric field creates a magnetic field and a changing
magnetic field creates an electric field. So if you setup a changing electric
field in a specific way, you can setup a cycle between the two field types.
Now, these fields hold energy and by virtue of this cycle, become capable of
carrying away this energy - what we call "light" - just as waves on water
carry energy away from the starting point at a certain speed. The strange
thing about E and B though is that this "speed" is a constant that is
independent of the reference frame you choose to monitor it. In other words,
this wave would move at the same speed relative to you no matter how you
happened to be moving and you can therefore never "catch up" with it.
Therefore no "thing" (matter) can move faster than light. \--

In physics, recursive "why"s always lead to "that's the way it is"
tautologies. For instance, if atoms are mostly empty space, why don't we fall
through the floor? Pauli figured out that no two fermions with same spin state
can occupy the same space. Why can't fermions do that? They are spin-1/2
particles and their wave function amplitudes cancel out if you account for the
fact that fundamental particles of the same type are indistinguishable. Why
does the combined wave function cancel out? .. 'cos that's what seems to agree
with experiment - i.e. because you don't see people falling through floors.

Progress seems to be about trying to extend this "explanation chain" by one
step more. So string theory can step in and add "because vibrating strings,
which is what we're made of, behave like this" .. and then it stops at some
point again.

------
Steuard
Two comments. First, as she alludes to in her edit, the "rotated arrow"
picture that RobotRollCall uses here is subtly backward. It does suggest the
right things and I used to think of it that way, but it eventually gets you in
trouble. (In actuality, as you start to move through space, your motion
through time _speeds up_... but this still leaves your arrow the same length
because the geometry of space-time is hyperbolic: the Pythagorean theorem
reads "x^2 - t^2 = c^2" instead of "x^2 + t^2 = c^2". This ends up avoiding
LOTS of issues, some of which were stumbling blocks for people in the comments
to her post. But it's certainly harder to visualize!)

Second, several people have complained that RRC avoided the underlying
question by saying "the arrow is always the same length". I think they may not
be giving that answer the credit it deserves. Her claim isn't that the speed
of light is the longest possible arrow (which I agree wouldn't help at all),
but rather that _every_ object's arrow has exactly this same length. That
shifts the speed of light from being an arbitrary constraint to being simply a
label for this universal fact. The question "Why is every arrow the same
length?" is still valid, but there's much less reason to worry about it: no
known process can change that length, just as no known process can change the
rest mass of an electron.

~~~
Steuard
It doesn't stand on its own terribly well without some substantial discussion
in class to back it up, but here's a handout that I've given to classes to try
and discuss this stuff a little:
[http://othello.alma.edu/~jensens/teaching/classes/spacetime....](http://othello.alma.edu/~jensens/teaching/classes/spacetime.pdf)

------
Jun8
No answer can be given to this question, it is one of the _axioms_ of
relativity theory. The explanation is trying to explain the axiom in terms of
the theory built on it.

I found these answers to be more informative:
[http://physics.stackexchange.com/questions/2230/why-and-
how-...](http://physics.stackexchange.com/questions/2230/why-and-how-is-the-
speed-of-light-constant)

------
hammock
The top answer on Reddit was not helpful to me, and seemed tautological even
in the face of its length.

WHY can't the arrow stretch? That is the crucial question; that is the
original question. The original question was not "is there/why is there a
tradeoff between space and time." The question was "Why can't the arrow
stretch, why can't we go faster than light allows?"

------
thret
I found her lengthy explanation patronising and unhelpful.

"you change your direction of motion through spacetime, but not your speed of
motion through spacetime."

This is article a long-winded way of restating the question, and leaves the
reader thinking they know the answer when they simply have a different
understanding of the same problem.

~~~
tel
Yeah, but a _mis_ understanding that's somewhat closer to the truth than
before. Unless you want to explain Minkowskian spacetime, hyperbolic rotation,
and its connection to Maxwell's equations... I think that coupling "motion
through time" and "motion through space" like she explains is a good step
forward from "cosmic speed limit".

------
ScottBurson
I would just explain that a photon has zero mass, but nonzero energy and
momentum and finite velocity. Intuitively (meaning: in a Newtonian universe),
one would think that a particle with zero mass would have to have infinite
velocity to have nonzero energy and momentum, right? And yet, its velocity is
finite. That demonstrates that the universe is not Newtonian. It also sets up
an intuitive connection (which is what we're looking for here, right?) between
the speed of light and one's intuitive sense of an infinite velocity.

Again, of course, this brings us to the question of why the universe is this
way: why it is Einsteinian rather than Newtonian. But that question really
belongs to the realm of metaphysics, not that of physics.

~~~
ars
Actually that question is easy to answer.

The universe is Einsteinian because otherwise e could not equal mc2.

And if that were the case then stars could not shine, and a TON of other
things would not work. Atoms could not exist either.

The reason is that as you go faster you have more energy (obviously) and since
you have more energy your mass increases. Since your mass increases you need
even more energy to increase your speed (since now you weigh more).

Take that to the limit and you find that as you reach the speed of light your
mass goes to infinity.

So it's necessary that it's impossible to exceed the speed of light - for
example if you had two objects each traveling at 51% of the speed of light
(relative to third placed in between them). Then relative to each other they
are going faster than light - which means they have more than infinite energy.

Can't do that.

So relativity is necessary if you want mass to be interchangeable with energy.

~~~
diziet
You mean to say they will be approaching each other at 81%~ speed of light.

<http://en.wikipedia.org/wiki/Velocity-addition_formula>

Surely you must read up on modern physics a little bit, sir!

~~~
ars
That's the point - because relativity exists, the measured speed is not simply
the addition of the two.

I was explaining why that is necessary if you want e=mc2

~~~
diziet
The way you'd phrased it confused the matter further, though. I'd consider
rewording some of it.

~~~
ars
So it's necessary that it's impossible to exceed the speed of light.

For example if you had two objects each traveling at 51% of the speed of light
(relative to third placed in between them). You only gave them a certain
amount of energy, but if speeds were additive and you compared them then it
would appear that their comparative speed was greater than the speed of light!

And that would imply an infinite amount of energy, which would be a problem.

Even if they were each traveling at 49% of the speed of light, so there are no
issues of infinity, it takes a lot less energy to accelerate two object to 49%
of the speed of light than it does to accelerate one to 98% of the speed of
light (because it's a lot heavier when it's going that fast, so it contains
far more energy), so you would have issues with conservation of energy.

Because of all that, speeds are not additive, and they get adjusted in a way
that keeps conservation of energy exactly correct.

Therefor relativity is necessary if you want mass to be interchangeable with
energy.

~~~
diziet
I understand that you say that they're not additive, but I have a feeling you
aren't really understanding what the actual math behind it is. Two objects
traveling at 51% the speed of light relative to a third object placed between
them (or anywhere else) would STILL travel at 81% the speed of light relative
to each other.

Please take a look at a very simple relativity homework solution to see if you
misunderstand the math or the concepts of relativity (that happens to be the
top result for "two spaceships approach each-other" on
google)[http://www.phy.duke.edu/courses/143/homework/hmwk3_solutions...](http://www.phy.duke.edu/courses/143/homework/hmwk3_solutions.pdf)
[It's problem #2]

~~~
ars
You are utterly missing my point.

I'm trying to show why relativity is necessary, I'm not trying to explain
relativity.

I'm giving an alternate universe where relativity does not exist and showing
why that universe could not work. And because it does not work, relativity is
necessary.

Please go back to the original question I am answering: Someone wanted to know
why the world is Einsteinian not Newtonian.

------
rdtsc
What helped me with a better understanding of time dilation is short paragraph
from RobotRollCall:

"""

If you're moving through space, then you're not moving through time as fast as
you would be if you were sitting still. Your clock will tick slower than the
clock of a person who isn't moving.

"""

~~~
ars
Maybe it helped you, but it's utterly inaccurate and incorrect.

There is no such thing as "moving through space". There is only moving
relative to another object. And BOTH of your clocks tick slower! Relative to
each other.

~~~
stephth
"[...] it's utterly inaccurate and incorrect. There is no such thing as
"moving through space"."

I think you're missing the point here. She's not trying to teach people the
perfect semantics, she's trying to progressively teach them concepts that are
tricky to understand and assimilate, step by step. And in a way they can
relate to.

By the way, she addresses what you brought up in her first followup (with yet
another compelling and easy to understand explanation).

~~~
ars
This is not a matter of semantics, if you ever want to understand relativity
the FIRST thing you need to do is get rid of the concept of absolute motion.
As long as you think in those terms you will never be able to understand it.

And addressing something in a followup is no good - fix your initial post to
be correct in the first place. Reddit allows you to edit your post.

~~~
stephth
If she had started by explaining relativity her post would have been twice the
size and she would have lost half the audience. Doesn't it matter to you that
people were actually interested in the topic and participative?

And why is a follow up no good? She didn't follow up to fix anything. She
followed up to follow up. (And mentioned it by, yes, editing her article).

~~~
burgerbrain
The problem here is that when explaining things improperly to be "good enough"
you have to be very very careful to make it clear what you're doing.

In my opinion, she failed to properly do that and crossed the line between
"helpfully simplifying" and "incorrect".

~~~
stephth
I went through your comments and you mentioned that "in a nutshell" the fact
that there's no such thing as a full stop in space is why "this explanation is
actually doing a disservice". But that's confusing to me because she clearly
stated - relatively to motion - "Those things are true, but we're ignoring
that kind of stuff right now."

Can you point out exactly where she crossed the line in your opinion?

~~~
burgerbrain
The confusion being expressed among commenters here is what I'm basing my
assertion off of. Simplification is fine, but I think in this case it pretty
clearly set a lot of people down the wrong track.

~~~
prawn
Some confusion is to be expected. After all, a lot of the concepts are pretty
tough to comprehend cleanly.

------
nazgulnarsil
Awesome explanation. But what I've never understood is what the universe looks
like to photons. What does it mean for a photon to travel between two points
from the frame of reference of the photon?

~~~
ars
Time does not exist for the photon, so from the photons point of view it is at
both locations simultaneously.

~~~
nazgulnarsil
erm, i looked up the answer. frames are inertial, thus photons don't have a
frame of reference.

~~~
ars
How so? Photons are inertial - meaning non-accelerating.

------
sambeau
Stephen Hawking predicted that things can travel faster than the speed of
light through quantum uncertainty. This is how information can escape from a
black hole.

<http://en.wikipedia.org/wiki/Hawking_radiation>

Put simply it works like this: light travels at a constant speed, but due to
quantum uncertainty nothing is in one exact place, it 'teleports' around an
average point. Thus, if it 'teleports' in the direction that the light was
travelling it has moved faster than the speed of light.

~~~
aerique
So this would mean that _on average_ nothing can travel faster than the speed
of light?

~~~
ars
No, it means that the quantum world is very very weird.

It's a strict limit, not an average. It's just that the quantum world has
strange definitions of location.

------
jerf
Another way to look at it that is arguably simpler (and with greater loss, of
course): Imagine the XY plane with every point described by integers in both X
and Y marked. That is, (0, 0), (1, 4), (-2, -5), etc. Connect each of them to
their four neighbors with a line segment. Now suppose you are at (3, 4) and
you want to move to (4, 5), and you may only use the lines given to you. You
move to the right, you move up, you're there. And you can move the other way,
too, all the line segments are bi-directional.

That works in space; that does not work in time. You can't stop moving or
change direction in time. You can put X and Y on that grid and have something
meaningful, but you can't say it's X and T; that would imply the ability to
freely move back in time or forward at your discretion, which is not true.

A simplified explanation of space and time's actual shape is that when you are
at (3, 4) and you are moving through time (in the first coordinate, let's
say), you've got lines that lead to (4, 4.1) and (4, 3.9) and so on, but the
lines only go to a certain angle, which for simplicity's sake I'll say is the
obvious 45 degree angle, which means you've got lines that go to (4, 3) and
(4, 5), but nothing else below 3 or above 5. You can only move along those
lines, and as there is no line to (4, -2) from your start position, there is
no way to get there. The bound of those lines is the speed of light. The
pictures of the "light cone" you may have seen are in some sense not merely a
helpful picture but actually a true picture of the universe.

You can not move faster than the speed of light because you can only move
between connected points in the universe, and to move faster than the speed of
light is to bypass that restriction. The universe is literally not shaped that
way. The shape of the universe forbids faster-than-light. You don't have any
choices other than those lines and none of the lines go faster than light.

This is a grotesque simplification, but I think the core point is accurate.
Exceeding the speed of light is impossible for reasons above and beyond the
mere "exceeding the speed of sound" or other things were. To travel faster
than the speed of light requires _changing the shape of the universe_. (And to
the extent that certain theories permit it under some circumstances, such as
the Alcubierre drive theory[1], I suspect that we'd find that even if we could
implement one of these things the universe would still find a way not covered
in those theories to shut it down, cosmic-censorship-style[2], or like [3]. I
would also note that all "practical" FTL drives proposed to date have
inevitably required the existence of at least one impossibility, such as
stable negative mass, and it means little to prove that if I have one
impossibility like stable negative mass I can have another like FTL.)

Also, because this is a grotesque simplification, please note that picking
apart holes in my picture is not even remotely the same as picking apart holes
in the theory of relativity, let alone picking apart holes in the Universe. In
particular don't get caught up with things that may appear to be going
backward; that's an illusion of this attempt to embed an explanation into
Euclidean space, not a real problem with the physics.

[1]: <http://en.wikipedia.org/wiki/Alcubierre_drive>

[2]: <http://en.wikipedia.org/wiki/Cosmic_censorship>

[3]: [http://books.google.com/books?id=_mo4AAAAIAAJ&pg=PA132&#...</a> (reading
pages 132 and 133)

------
boh
I remember reading an article a while back:

"Scientists Make Radio Waves Travel Faster Than Light"

article:

[http://www.universetoday.com/33752/device-makes-radio-
waves-...](http://www.universetoday.com/33752/device-makes-radio-waves-travel-
faster-than-light/)

the paper it's based on:

<http://arxiv.org/abs/physics/0405062>

Anyone with a Physics background care to comment on the validity of this
study?

------
statictype
She's got a lot of good stuff in her comment history.

I really wish Instapaper worked with reddit comments. Lots of good reading
there.

------
adobriyan
My gut feeling is that article is dragged :-) into somewhat irrelevant things
like Poincare group et al.

Why maximum limit exist at all? How Universe without this limit will look
like? How Universe with limit which is not equal to speed of light will look
like?

Antropic principle inevitably pops up.

~~~
ars
See my answer here: <http://news.ycombinator.com/item?id=2244559>

In order for e=mc2 you are required to have relativity. And a world without
that could not exist.

------
olalonde
This explains why there's a limit to speed but not why this limit is light's
speed.

~~~
augustl
Afaik the answer is that the limit is the limit, and the speed of light is
unlimited - but there is a limit, so the speed of light is the same as the
fastest speed possible. So the limit is not the light's speed, they just
happen to be the same.

------
retube
What I want to know is what happens if the arrow is rotated more than 90
degrees?

------
sliverstorm
eh, it's more fun to imagine we will one day surpass the speed of light. It
hasn't been disproved so conclusively that I know about said proof, so as of
yet I can continue imagining the barrier will be broken.

~~~
83457
I like the way the Asimov talks about hyperspace, a currently unknown
dimension that allows for "jumping" through/over huge segments of space
without technically traveling faster than light, completely circumventing the
issue of faster than light travel and extreme time dilation.

------
joelmichael
If you were moving in a "completely horizontal" direction, wouldn't you not be
moving through time at all, but only through space? That means you could move
infinitely fast, not with a strict limit.

~~~
uvdiv
Yes, but that kind of motion (tachyonic) is unphysical. It violates causality:
you can imagine that by "rotating" the "horizontal" motion very slightly
"downwards", in a different reference frame it is backwards time travel.

The salient thing is that there are three disconnected classes of 4-vectors:
timelike (massive particles), spacelike (tachyons), and lightlike (massless
particles). Lorentz coordinate transforms can only take you between 4-vectors
of a particular type: e.g. there's no inertial reference frame where timelike
motion looks like tachyonic motion.

------
rbanffy
It's a good explanation, really, but do we need to have only one? Can't we
keep Reddit things in Reddit and HN things in HN?

If I am in a Reddit mood, I will go to Reddit. If I'm more in a HN mood, I
will come here.

~~~
biot
Following your argument to its logical conclusion, HN should stop linking to
external sites because if people are in a _site X_ mood, they will go to _site
X_ , for any value X.

For myself, I don't visit Reddit unless there's something interesting linked
to from elsewhere, such as HN. Thus, I appreciate this being posted to HN.

~~~
rbanffy
> HN should stop linking to external sites because if people are in a site X
> mood, they will go to site X, for any value X

Your reasoning is flawed. The value of HN is its community and the discussions
it's capable of spawninf. There are sites for discussing an ampler spectrum of
subjects (like, for instance, the nature of the universe and laws of physics)
and sites for discussing news that interest specifically to hackers (according
to the definition implied in the "Hackers and Painters" book).

~~~
SoftwareMaven
And that argument is exactly why the comment should be linked here. If the
Reddit comment had been a blog post, everything would have been fine, right? I
want to see the comment and get to stay here for the conversation.

------
cgart
Oh, finally we got here cool discussion. Here is how I explain that one
"could" travel faster then the speed of light! HOWEVER, and this is VERY
IMPORTANT, this depends on your definition of the speed. So imagine following
experiment:

There are two space ships which are built like these russian matroshkas. One
smaller space ship is in the hangar of a bigger one. The bigger one starts
from the earth and accelerates to the speed of light (or just until 0.999c).
Now, the smaller ship starts and can again accelerate from the bigger ship
point of view until 0.999c. So, if there is just a simple velocity measure
instrument, which is measuring acceleration by F = m*a, and we know the
relative space ship mass "m" as it was relative to the earth, then knowing how
much force our engine produces we can compute the acceleration. And hence our
velocity measurement device will add small "a" to the current velocity by
every thrust of the engine.

So given that type of measurement, our smaller space ship can accelerate to
the speed of 2c relative to the earth. HOWEVER, due to the relativistic
effects the people living on the earth would never ever realize that this ship
was moving with 2c, since they are measuring speed by looking how far the ship
went in the certain amount of time. And due to the time dilation they will
never realize that this ship was actually much farther away then it looks
like.

So, regarding to this experiment, we can travel faster then the light.
However, this is only due to the definition of the speed.

A counter argument would be that the mass "m" is also changing. However, one
could argue that the mass is represented by the amount of particles per volume
unit and hence remain constant if volume remain constant. Ok, another guy
could argue again that the size of the volume shrinks, but I could then argue
that if size of the volume shrinks, then the density of the particles per
volume unit from the earth point of view would increase and could end up in a
singularity or just black hole, so big bang ?:confused:

This kind of experiment fits well into my experience of the world, where I
just cannot accept some of the constraints we get from the nature :) Yes, you
cannot travel faster then the speed of light, BUT this is only because I stay
at the earth and measure your speed by looking how fast you come back. But
this pure guy who is traveling could measure the speed as I've proposed and
would then realize that, in deed he was faster then the "earth's speed of
light" :)

~~~
CJefferson
Unfortunately, you are trying to impose a traditional world, where speeds are
additive, onto relativity. It just doesn't work that way. A light beam fired
from Earth would overtake the smaller ship, so in Earth's frame it is going
slower than the speed of light.

~~~
cgart
Yes, you are right, but you just didn't get the point what I was trying to
say. In deed I was expected that I will be downvoted by this comment :)

I never claimed that speeds are additive. I've just claimed that it fully
depends on what you define as a speed. If you define the speed the classical
way (space unit per time), then due to the relativistic effects, it will never
work out for you.

However, and this is the point, if you define the speed as just some counter
running in front of you which add a value on every engine thrust, then it will
work out for you that you are traveling faster, then the "earth's" speed of
light!!!

Imagine just another experiment. You are waking up at a space ship and there
is nothing around you where you can fix your view to see if you are moving or
not. So, the speed-counter on this ship shows you 0.9c (here c is "earth's
c"). No, you press the accelerate button and accelerates to additional 0.2c.
There is nothing which would stop you accelerating, because in your frame you
can assume that you are at rest! So, adding now the new velocity amount to
your previous you get 1.1c, HOWEVER, this the "earth's c" ,so the speed of
light as it is measured on the earth!!! In your frame, since you have no clue
if you was moving or not, you should assume that you have now only 0.2c or
just 0c, since you cannot measure the speed in the classical way anymore
(there is no other point to fix on).

So, this is the way how to understand the relativistic effects. There is no
"super-dooper" spaghetti-monster hand, which will for some reason stop you
accelerating. No, this is just because everybody around you will never be able
to measure your real speed, because they can only measure the speed relative
to their frame.

------
vlisivka
Wave cannot travel faster than speed of wave in medium.

Matter is form of electromagnetic wave, thus matter cannot travel faster that
speed of electromagnetic wave in medium ("vacuum").

Everything that is not a form of electromagnetic wave, OR disconnected from
electromagnetic medium, will be not bound to speed of light.

Imagine water and water waves. Water waves will never travel faster than speed
of wave in water.

BUT, you can freeze water and push it faster than water wave just because it
is not a part of water anymore.

I hope, super-cold vacuum (below 0K) or matter in cocoon of super-cold vacuum
will be able to travel faster than speed of light.

PS.

Of course, I cannot even imagine, how we can freeze vacuum, because we cannot
even interact with it.

~~~
ars
The entire point of relativity is that there is no medium. There are plenty of
particles that do not interact electromagnetically - the neutrino for example.

The speed of light has to do with the nature of reality, not the method of
transportation.

~~~
vlisivka
Relativity is theory. We are talking about real world.

We already know, that vacuum can generate particles, thus it is not completely
empty:

[http://scienceblog.com/40901/theoretical-breakthrough-
genera...](http://scienceblog.com/40901/theoretical-breakthrough-generating-
matter-and-antimatter-from-the-vacuum/)

You can find much more information about faster than speed traveling here:
<http://en.wikipedia.org/wiki/Faster_than_light_travel> .

~~~
ars
Relativity describes the real world.

You seem to want to talk about theoretical ideas that have no evidence.

You quite misunderstood that article, it's not the vacuum that produces the
particles, it is the massive energy they are beaming that produces them.

The stuff in the wikipedia article is just ideas that may work mathematically
but have little bearing on the real world. At least for now. Maybe someday
we'll figure them out, but for now it's just ideas.

~~~
vlisivka
> Relativity describes the real world.

Any theory describes real world to some degree.

> You seem to want to talk about theoretical ideas that have no evidence.

:-/ We can test my ideas in your laboratory, of course.

> You quite misunderstood that article, it's not the vacuum that produces the
> particles, it is the massive energy they are beaming that produces them.

Do you really read article? Of course, energy is necessary, because two vacuum
particles will cannot escape each other and will annihilate. But you cannot
produce particle using just energy.

> The stuff in the wikipedia article is just ideas that may work
> mathematically but have little bearing on the real world. At least for now.
> Maybe someday we'll figure them out, but for now it's just ideas.

Some far galaxies are traveling from us much faster than speed of light
because of space expanding. Thus theory of relativity will work correctly for
distances less than 1B of light years, but it is not correct for larger
distances. Are you agree?

~~~
ars
"But you cannot produce particle using just energy."

Yes you can.

And no I don't agree with your last sentence.

~~~
vlisivka
No, you cannot.

Do you know about Big Bang?

~~~
ars
What do you want to know about the Big Bang?

And why in the world do you think you can not produce particles using just
energy? It happens all the time.

------
sabat
Good explanation of space/time -- in short, you're always moving in space and
time, and the more you move in space, the less you move in time. Vice-versa.

Brian Greene does a pretty good job of explaining all this in the Elegant
Universe. If you're into this kind of thing, check it out.

~~~
ars
But there is no such thing as moving in space.

You can only move relative to another object. You may even move fast relative
to one object and slow relative to another, meaning your clock ticks at a
different rate relative to each of those objects.

There is no absolute clock - you can only compare your clock with someone
else's clock.

~~~
heed
Can you move relative to a point in space? Even if there are no objects
around?

~~~
ars
No, because a "point in space" has no definition - without other objects you
can't even locate such a point.

You can only move relative to other objects.

------
tastybites
Does it work in the other direction, or can you only take away time velocity
to give to space velocity?

i.e., can you make your time slow down by coming to a full and complete "stop"
in space, since I assume nothing in the universe is truly at rest?

~~~
burgerbrain
_"So is there any such a thing as a complete and full "stop" in space"_

No, and that is why in a nutshell why this explanation is actually doing a
disservice.

~~~
stcredzero
No analogy is perfect, in particular many analogies are trying to link our
everyday experience with things that extend outside of it.

If we take this and your statement further, we could just declare that all
analogies are doing a disservice, and all pop science writers should be
flogged.

------
zrgiu
what I don't understand is why the light is the point of reference. Just
because it's the fastest "thing" we know ? Or is there some other reason ?

~~~
jarin
Photons and gluons are the only two particles that we know to be massless and
therefore capable of moving at the speed _c_ (some neutrinos might be
massless, but we know at least 2 of them are not).

Since gluons are never observed as free particles and we're all familiar with
photons, we call it the speed of light.

------
csomar
_The motion I'm referring to is motion in the futureward direction._

May be you should consider the fact, that while you are not moving- let's
assume that your are in space and way far from earth or any other thing-, your
brain, heart and blood do. If they don't, you wouldn't exist. It's in my
believe that we are living in a single dimension world, and it's not quite
different than a dream; actually it's the same thing. Just think about it ;)

