Speeds greater than the speed of light

[Austin0]

Hi Jake ( and welcome to PF )

I am using coordinate notation such that (x,t) is (distance,time)

Alice's frame (S)

Event A: Alice sends a superluminal signal at (0,0)
Event B: Bob receives the superluminal signal at (10,5)

The signal travels 10 lightseconds in 5 seconds (2c) in Alice's frame.

Bob's frame (S')

Event A' = (0,0)
Event B' = (x',t')

Using the Lorentz transformation

x^{\prime} = \gamma (x - vt)

t^{\prime} = \gamma \left( t - \frac{vx}{c^2} \right)

where \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}

Assume Bob is moving at 0.8c relative to Alice and units such that c=1.

\gamma = \frac{1}{\sqrt{1 - \frac{0.8^2}{1^2}}} = 1.666

x^{\prime} = 1.666 ( 10 - 0.8*5) = 10

t^{\prime} = 1.666 \left( 5 - \frac{0.8*10}{1^2} \right)= -5

________________________________________________________________________
Hi I apprecciated the clear cut presentation of the maths but couldn't help note a certain paradoxical self negation in your final derivation.
It appears to me that if the signal actually went back in time it couldn't possibly arrive at x=10 and conversely if it did arrive at x=10, it by definition was traveling forward in time no matter what the maths say.


There is the negative time interval: minus 5 seconds.

 

[DrGreg]

RandallB, re post #50

I'm trying to work out if there is any common ground between us, anything we can both agree on. That was the purpose of my post #48 and your dismissal of my entire post as "obviously flawed" doesn't help me in that objective. (By the way, what is "obvious" to you need not be obvious to anyone else, otherwise we wouldn't be having this discussion.) Let me spell this out in pedantic detail.

Here are some problems and solutions. I'd like to to consider each problem in isolation and tell me if you accept each solution, or, if not, why not. (All times are in seconds, all distance in light-seconds.)

Question 1: Relative to inertial observer Carol, H and K are the events

(T_H, X_H) = (0, 0)
(T_K, X_K) = (12, 48)​

Regardless of whether you think this is possible in the real Universe, if information were to travel from H to K, what would its speed be relative to Carol?

Answer 1: 4 (in the + direction).

Question 2: Relative to inertial observer David, L and M are the events

(T'_L, X'_L) = (-44, 64)
(T'_M, X'_M) = (-35, 28)​

Regardless of whether you think this is possible in the real Universe, if information were to travel from L to M, what would its speed be relative to David?

Answer 2: -4 (i.e. 4 in the - direction).

Question 3: Relative to inertial observer Elizabeth, P and Q are the events

(T''_P, X''_P) = (0, 0)
(T''_Q, X''_Q) = (-21, 0)​

Do you think all inertial observers agree that Q occurs before P? If not, give an example of an observer who disagrees.

Answer 3: Yes, all observers agree, because T'''_Q = \gamma(T''_Q - vX''_Q) = -21\gamma < 0, whatever the value of v and \gamma.

Question 4: Relative to inertial observer Alice, E, F and G are the events

(t_E, x_E) = (0, 0)
(t_F, x_F) = (12, 48)
(t_G, x_G) = (-21, 0)​

Bob moves at speed 4/5 relative to Alice (in the + direction) with clocks & distances synced such that in Bob's coordinates

(t'_E, x'_E) = (0, 0)​

What are the coordinates of F and G relative to Bob?

Answer 4:

(t'_F, x'_F) = (-44, 64)
(t'_G, x'_G) = (-35, 28)​

I know we are going to disagree at a later stage but can you please restrict yourself to commenting on the above 4 independent problems and let me know if you disagree with any of the solutions?

I've asked these questions so we can avoid wasting time arguing over things we agree on and concentrate on where we disagree.

 

[carstenk]

I'm a noob here and have a related question, or maybe it's the same one: Can the relative speed of two objects exceed the speed of light? I would assume so, for example the diametrically opposing objects on the edges of the observable universe that each move away from Earth at the speed of light. Grateful for you expert advice.

 

[Phrak]

There is a loophole, however...Lookup "Alcubierre Drive" on Wikipedia for more info.

Your loophole requires the existence of exotic matter.

 

[HallsofIvy]

I'm a noob here and have a related question, or maybe it's the same one: Can the relative speed of two objects exceed the speed of light? I would assume so, for example the diametrically opposing objects on the edges of the observable universe that each move away from Earth at the speed of light. Grateful for you expert advice.

No. In relativity speeds don't add like that. If object A is moving away from the Earth with speed .99c relative to the Earth and object B is moving in the opposite direction with speed .99c relative to the eath then the speed of each relative to the other would be
\frac{.99c+ .99c}{1+ \frac{(.99c)(.99c)}{c^2}}= \frac{1.98c}{1+.9801}
= .99994904975c still slightly less than c.

 

[azzkika]

Assume there is a circular device on the moon. it consists of laser activated propulsion plates that move a ball upon activation. now imagine this to be very big. then you shine a laser from Earth powerful enough to activate the plates. you then rotate it faster and faster until such time the beam that reaches the moon's surface is traveling faster than c across it's surface triggering the plates at greater than c speeds. would the ball travel faster than c??

 

[A.T.]

Assume there is a circular device on the moon. it consists of laser activated propulsion plates that move a ball upon activation. now imagine this to be very big. then you shine a laser from Earth powerful enough to activate the plates. you then rotate it faster and faster until such time the beam that reaches the moon's surface is traveling faster than c across it's surface triggering the plates at greater than c speeds. would the ball travel faster than c??

No. You could just as well ask if the ball would travel at infinite speed, if you trigger the platforms simultaneously.

 

[Mr.Amin]

I think this thread is done.

In nature, no phenomena has been observed to actually propagate faster then EM waves. Special relativity/general relativity, and the post-parameterized Newtonian models model near light speed behaviors quite well. Until superluminal phenomena are observed, this is a debate worthy of a coffee break. Mind you, even the most cooky theorists would not try to cook up things that refute observable nature--that is for mathematicians to explore.

IF there is such a thing, nature will eventually show us. Until then, c is c.

 

[azzkika]

No. You could just as well ask if the ball would travel at infinite speed, if you trigger the platforms simultaneously.

just out of curiosity, what speed would the ball achieve if such an experiment could be conducted?

And when approaching c, how much mass is gained as a ratio of itself of the actual ball?

Sorry to be a pain.

 

[334dave]

wow ..i have gone through a bag of popcorn reading this thread ..
first the org question concerns speed of light ..
it is my understanding that C is verabale .. ie in gravaty field water gas's diamond ect..
thus in "space" which is not empty it will change..
the vacuum speed ref.. should we not be considering the speed of a gamma partial ?
any way my real question of the moment is
a super lumen signal is energy of some kind [[which as we know is that e= mC thingy]]
\IF we assume that supper lumen singling is possible then is not time travel it self possible again due to that mater and energy are two sides of a sea saw?

an another question .. in my small mind as we approach C and mass increases would we not collapses to a micro black hole?

 

[Mr.Amin]

Alll right, I sent e-mails to the previous gent/lady "azzkika".

First, let's use what we know about the physical universe.
1) No signal can be sent at any rate exceeding that of light traversing a vacuum.
2) As you build "speed" (I hate that term), MASS is NOT generated.
3) Gravitational field curve space, they do not slow light trajectories.
4) Mass distributions (i.e. glass, dust, water) transparent to light slow light BECAUSE their electrons interact witht the light. Remember you lessons on polarization and complex susceptibility.

SO
1) Even if you could say get in front of an electromagnetic signal, what use is it since the you have not intercepted the signal. Causality still holds. Superluminal signals have nothing to do with "time travel" unless you are speaking of going forwards.

2) E=mc^2 does not mean that MASS increases when kinetic energy increases. The equation is fully written with a relativistic gamma multiplying the rest mass, m_0. It is the momentum that you are fighting to go faster. The change in momentum is what skyrockets. This is why it takes so much energy to go from 0.99c to 0.999c. Therefore, even if you could get a Ferrari traveling near c, you would not get a black hole. See Schutz's book or Misner Thorne and Wheeler's book. This interpretation took a little longer to understand.

3) Light always travels along null trajectories. This means that electromagnetic waves irrespective of wavelength (power line through hard gamma) travel the SAME route in a vacuum. For those of you who would ask about refractive effects, remember refraction requires charges to be present.

4) This is suitable for another thread or is nicely explained in "Modern Optics" by Fowles.
It is also in Jackson, for those daring enough.

 

[334dave]

first:

No. In relativity speeds don't add like that. If object A is moving away from the Earth with speed .99c relative to the Earth and object B is moving in the opposite direction with speed .99c relative to the eath then the speed of each relative to the other would be
\frac{.99c+ .99c}{1+ \frac{(.99c)(.99c)}{c^2}}= \frac{1.98c}{1+.9801}
= .99994904975c still slightly less than c.

wow .. you know i kinda thought the question was a good one.
i have never understood that before..
should have gone to collage i guess..

Alll right, I sent e-mails to the previous gent/lady "azzkika".
First, let's use what we know about the physical universe.
1) No signal can be sent at any rate exceeding that of light traversing a vacuum.

oh i agree, in my small mind the only way to seem to excede C would be folding or worm holes

2) As you build "speed" (I hate that term), MASS is NOT generated.
3) Gravitational field curve space, they do not slow light trajectories.

ugh here i agree- i referring to appearance time laps of that light from egality two diff sources one will arrive later due to the apparent effects of the gravity fields between us and sorce and the other source has no gravity wells between us..
ie if space it self is warped then ther is an appearent streching

4) Mass distributions (i.e. glass, dust, water) transparent to light slow light BECAUSE their electrons interact witht the light. Remember you lessons on polarization and complex susceptibility.

SO
1) Even if you could say get in front of an electromagnetic signal, what use is it since the you have not intercepted the signal. Causality still holds. Superluminal signals have nothing to do with "time travel" unless you are speaking of going forwards.

2) E=mc^2 does not mean that MASS increases when kinetic energy increases. The equation is fully written with a relativistic gamma multiplying the rest mass, m_0. It is the momentum that you are fighting to go faster. The change in momentum is what skyrockets. This is why it takes so much energy to go from 0.99c to 0.999c. Therefore, even if you could get a Ferrari traveling near c, you would not get a black hole. See Schutz's book or Misner Thorne and Wheeler's book. This interpretation took a little longer to understand.

humm seems i must have skimped that day.. as i thought that as you neared C yur mass increased.. will have to attempt correcting this miss understanding..
thanks for bringing it to my attention..

3) Light always travels along null trajectories. This means that electromagnetic waves irrespective of wavelength (power line through hard gamma) travel the SAME route in a vacuum. For those of you who would ask about refractive effects, remember refraction requires charges to be present.

4) This is suitable for another thread or is nicely explained in "Modern Optics" by Fowles.
It is also in Jackson, for those daring enough.

 

[carstenk]

No. In relativity speeds don't add like that. If object A is moving away from the Earth with speed .99c relative to the Earth and object B is moving in the opposite direction with speed .99c relative to the eath then the speed of each relative to the other would be
\frac{.99c+ .99c}{1+ \frac{(.99c)(.99c)}{c^2}}= \frac{1.98c}{1+.9801}
= .99994904975c still slightly less than c.

Thanks for your clear answer, which aligns with other explanations I have seen. I have great difficulties in accepting it though, as it obviously defies logic. I would think that since object A and object B are not interrelated in any way they would simply be invisible to each other once their relative velocities exceed c. One interesting implication of your answer also seems to be that everything in the universe is visible to us, because nothing will ever escape the event horizon due to relative velocities exceeding the speed of light.

But these are obviously just my amateurish speculations, and that's usually put to rest by empirical evidence. It's hard to imagine empirical evidence for something we can't see, but is the inverse may have been proven (that we never loose sight of anything)? grateful for the direction to some such experiment in that case.

 

[A.T.]

I have great difficulties in accepting it though, as it obviously defies logic.

It doesn't defy logic, just intuition and presumptions. Pure logic alone doesn't tell you how nature behaves.

 

[JesseM]

Thanks for your clear answer, which aligns with other explanations I have seen. I have great difficulties in accepting it though, as it obviously defies logic.

It may seem less illogical if you understand that each observer defines "speed" in terms of distance/time on rulers and clocks at rest relative to themselves, and that each observer also measures the rulers and clocks of other observers to be distorted (rulers shrunk, clocks slowed down). So, the fact that a third observer sees A and B separating at faster than the speed of light does not imply that A and B measure each other to be moving away faster than light.

I would think that since object A and object B are not interrelated in any way they would simply be invisible to each other once their relative velocities exceed c. One interesting implication of your answer also seems to be that everything in the universe is visible to us, because nothing will ever escape the event horizon due to relative velocities exceeding the speed of light.

The formula above is only intended to work in special relativity where spacetime itself doesn't behave in a dynamical way--in general relativity where spacetime is curved by mass, there actually can be an event horizon between sufficiently distant galaxies because the space between them is expanding faster than a light beam can bridge the gap (see http://www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03 for some more on this).

 

[Ich]

I would think that since object A and object B are not interrelated in any way they would simply be invisible to each other once their relative velocities exceed c.

Well, the whole point of HallsofIvy's answer is that relative velocities never exceed c. So I don't see where your difficulties come from - except that you maybe hadn't time to read carefully, as you answered hastily.

 

[cyberfish99]

Don't say definitely that no matter can go faster than the speed of light. There is always the theoretical sub-atomic particle, the tachyon. For a quick overview, http://en.wikipedia.org/wiki/Tachyon"

 

[JesseM]

Don't say definitely that no matter can go faster than the speed of light. There is always the theoretical sub-atomic particle, the tachyon. For a quick overview, http://en.wikipedia.org/wiki/Tachyon"

Tachyons can't be ruled out absolutely, but they'd violate either relativity or causality (meaning you could use them to send messages into the past). See the discussion on this thread for example.

 

[carstenk]

The formula above is only intended to work in special relativity where spacetime itself doesn't behave in a dynamical way--in general relativity where spacetime is curved by mass, there actually can be an event horizon between sufficiently distant galaxies because the space between them is expanding faster than a light beam can bridge the gap (see http://www.scientificamerican.com/article.cfm?id=misconceptions-about-the-2005-03 for some more on this).

Thanks for your patient explanations, which is highly appreciated. Unfortunately the article on Scientific American that you refer to requires a paid subscription that I currently can't justify. But your answer is interesting, since it in fact seems to (politely) refute HallsofIvy's original explanation, and in fact say that relative speeds (based on the expanding universe at least) above the speed of light is indeed possible in the scenario I originally described, since the farthest observable objects on diametrically opposite sides of the Earth are indeed escaping at the speed of light because of the expanding universe. I'm just puzzled that this is not advertised more, because I had known I would obviously not have asked my original question, and a lot of the discussion here could instead concentrate on the implications of the cases where c is actually exceeded.

 

[JesseM]

Thanks for your patient explanations, which is highly appreciated. Unfortunately the article on Scientific American that you refer to requires a paid subscription that I currently can't justify.

Sorry, I didn't notice that, it had been free for a long time...anyway I found a free PDF copy on an MIT page here:

http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf

But your answer is interesting, since it in fact seems to (politely) refute HallsofIvy's original explanation, and in fact say that relative speeds (based on the expanding universe at least) above the speed of light is indeed possible in the scenario I originally described, since the farthest observable objects on diametrically opposite sides of the Earth are indeed escaping at the speed of light because of the expanding universe. I'm just puzzled that this is not advertised more, because I had known I would obviously not have asked my original question, and a lot of the discussion here could instead concentrate on the implications of the cases where c is actually exceeded.

The problem is that to deal with cosmological scenarios we have to deal with non-inertial coordinate systems, while the restriction that nothing can travel faster than c is only intended to apply in inertial frames, the way that we can define a non-inertial coordinate system in GR is totally arbitrary (you could define a coordinate system where you were moving faster than c relative to some object in your own room, for example, although presumably light itself would move even faster in such a coordinate system). In general relativity all large-scale coordinate systems are non-inertial, one can only define "local" inertial frames in very small neighborhoods around freefalling observers, a consequence of the "equivalence principle" which is discussed in http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html .

 

[cfrogue]

Sorry, I didn't notice that, it had been free for a long time...anyway I found a free PDF copy on an MIT page here:

http://space.mit.edu/~kcooksey/teaching/AY5/MisconceptionsabouttheBigBang_ScientificAmerican.pdf


The problem is that to deal with cosmological scenarios we have to deal with non-inertial coordinate systems, while the restriction that nothing can travel faster than c is only intended to apply in inertial frames, the way that we can define a non-inertial coordinate system in GR is totally arbitrary (you could define a coordinate system where you were moving faster than c relative to some object in your own room, for example, although presumably light itself would move even faster in such a coordinate system). In general relativity all large-scale coordinate systems are non-inertial, one can only define "local" inertial frames in very small neighborhoods around freefalling observers, a consequence of the "equivalence principle" which is discussed in http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html .

I must ask the experimental basis for this conclusion.

 

[JesseM]

I must ask the experimental basis for this conclusion.

A coordinate system isn't defined by experiment, it's just a way we choose to label events in spacetime, we can define it however we want. And purely as a theoretical matter, it's possible to show that if the tensor equations of GR work in one coordinate system in a given spacetime (say, Schwarzschild coordinates in a black hole spacetime), they will be unchanged under a totally arbitrary coordinate system (such an arbitrary transformation is called a diffeomorphism, and the equations of GR are 'diffeomorphism invariant').

 

[cfrogue]

A coordinate system isn't defined by experiment, it's just a way we choose to label events in spacetime, we can define it however we want. And purely as a theoretical matter, it's possible to show that if the tensor equations of GR work in one coordinate system in a given spacetime (say, Schwarzschild coordinates in a black hole spacetime), they will be unchanged under a totally arbitrary coordinate system (such an arbitrary transformation is called a diffeomorphism, and the equations of GR are 'diffeomorphism invariant').

Yea, you can do whatever you want.

I would like to see an experiment to verify this assertion.

There must be a way to perform a comparison.

 

[JesseM]

Yea, you can do whatever you want.

I would like to see an experiment to verify this assertion.

What assertion? Do you want an experiment to verify the assertion that we humans are free to label events with whatever coordinates you want (which isn't a physical claim so it would make no sense to demand experimental evidence for it), or do you want an experiment to verify that the equations of GR is diffeomorphism-invariant? (which is a purely mathematical matter so it doesn't require experiments either, any more so than the claim the Maxwell's laws of electromagnetism are Lorentz-invariant...the only thing you might test experimentally are whether the equations of GR or Maxwell's equations are actually the correct ones to describe the physical world, but even if they turned out to be incorrect, it wouldn't change the fact that the equations of GR are diffeomorphism-invariant and Maxwell's equations are Lorentz-invariant)

 

[cfrogue]

A coordinate system isn't defined by experiment, it's just a way we choose to label events in spacetime, we can define it however we want. And purely as a theoretical matter, it's possible to show that if the tensor equations of GR work in one coordinate system in a given spacetime (say, Schwarzschild coordinates in a black hole spacetime), they will be unchanged under a totally arbitrary coordinate system (such an arbitrary transformation is called a diffeomorphism, and the equations of GR are 'diffeomorphism invariant').

I have it now.

You cannot travel faster than the speed of light in this "coordinate system".

 

[JesseM]

I have it now.

You cannot travel faster than the speed of light in this "coordinate system".

Let's put it this way: if you are inside an expanding light sphere, you can never outrun the light and escape the sphere, regardless of what coordinate system is used. Your own coordinate speed may be greater than the coordinate speed of light at some position, though (for example, in Schwarzschild coordinates the speed of light approaches zero at the event horizon, so observers far away from the horizon can certainly travel with a greater coordinate speed than light close to it).

 

[cfrogue]

Let's put it this way: if you are inside an expanding light sphere, you can never outrun the light and escape the sphere, regardless of what coordinate system is used. Your own coordinate speed may be greater than the coordinate speed of light at some position, though (for example, in Schwarzschild coordinates the speed of light approaches zero at the event horizon, so observers far away from the horizon can certainly travel with a greater coordinate speed than light close to it).

Pretty funny.

You explain it in a way we are operating.
Yes, I get this.

 

[Mihael@@/&]

Love physics but had a bad teacher in math.
quick question: where to find: -If we go with speed of light we will be faster than any photon

 

[Dale]

where to find: -If we go with speed of light we will be faster than any photon

In the science fiction section of your local library.

 

[Mihael@@/&]

And how many ours have you thought about that? Or who proved it? Let's sacrifice him:)

 

[Dale]

Or who proved it?

I believe it was either Einstein or Minkowski, but I don't have a reference.

 

[heldervelez]

The limiting 'c' value is not proved 'per se'.
It was 'postulated' at SR, and as any other postulate it is not proved but assumed.

The Maxwell equations already have it.
Long before Einstein it was known that light and energy transfers (namely photons) can travel at most at a limiting value.

The first quantitavive measurement: "[URL (1676)[/URL]

In any material this relation holds: c^2=1/( ε/μ ) where
μ is the magnetic constant or permeability
ε, permittivity or electric constant
ε0 and μ0 if related to vacuum.

All the measurements made in the past obtain a limiting value to 'c'.
But 'c' is not at all a 'constant'. It is dependent on the medium(*) and the gravitational field.

The permeability and the permittivity (and 'c') are 'properties' of space (or medium) that dictates the rate of change of energy transfers (and information exchange).

------
If it is possible an 'infinite speed' of light then all 'causes' and 'effects' would existed at once, without a relation, and all past (and future) events would have existed in that single instant of 'no duration'.
A magical place where anything (or nothing ?) could exist.
If infinite speed brings un unlawfull universe then some limit must exist. 'c' its ok.
Frustating ? blame the 'space' or its creator ;) !
------

(*) in a Bose-Einstein condensate (at extremely very low temps) the photons almost stop.

 

[Dale]

The limiting 'c' value is not proved 'per se'.
It was 'postulated' at SR, and as any other postulate it is not proved but assumed.

That is not quite correct. SR postulates that c is the same in all reference frames (frame invariant). That a material object is limited to speeds < c is then a derived result from the postulates.

 

[stevmg]

If one is in inertial frame S and another inertial frame S' is moving to the right at just a "tad" below the speed of light and a third intertial frame S"" is moving relative to S' at a "tad" below the speed of light, the velocity of S" relative to S is still just a "tad" below the speed of light or c. This is by the Lorentz equations used by Einsteing to combine velocities:
(v1 + v2)/(1 + v1*v2/c^2) where v1 and v2 are speeds a "tad" below the speed of light.

If a Big Bang occurred 13 billion years ago, then the advancing edge would be 13 billion years old and 13 Billion light years away. A second advancing edge on top of the first advancing edge would also be 13 billion light years away but the combined distance from the original center would still be only 13 billion light years away from the origin and also 13 billion light years from the other leading edge. We would thus have a circular universe as the path from the original center to the second "leading edge" would still be only 13 billion light years and could not go through the first leading edge.

Does anyone follow what the hell I am saying?

 

[Ich]

Does anyone follow what the hell I am saying?

Not really, but I'm familiar with the Milne model, and I think that's what you're talking about.

If a Big Bang occurred 13 billion years ago, then the advancing edge would be 13 billion years old and 13 Billion light years away.

That's true if we neglect gravity and decribe the universe in standard minkowski coordinates instead of cosmological ones. The "edge" is the future light cone of the Big Bang event then, the position where the very first photons are.

A second advancing edge on top of the first advancing edge would also be 13 billion light years away but the combined distance from the original center would still be only 13 billion light years away from the origin and also 13 billion light years from the other leading edge.

No, there is no second edge. The details of "distance to the edge" are a bit tricky for different observers (because of simultaneity issues), but nonetheless it is one and only one light cone.

 

[stevmg]

To Ich...

I never said I was a genius.

I stated it backwards:

Imagine a point S at the theoretical beginning of time. Then BOOM! Along comes a Big Bang. Say point A flies out to the right at light speed, c.

Also, Point B flies to the left at light speed c. Now, what is the separation speed of points A and B?

Guess what! It is still c.

Now we are 13 billion years down stream and point A is 13 billion lightyears from S (although we never know what S is), and point B is 13 billion light years from point S the other way. A and B are still only 13 billion light years apart. You can't go through S to get from A to B because that would be bigger than 13 billlion light years hence, point S, A and B are on a great circle each 13 billion years from each other. There must be a fourth dimension to create this monstrosity.

I tell you, Hugo Lorentz and Albert Einstein made so many things uninterpretable...

 

[Fredrik]

Imagine a point S at the theoretical beginning of time. Then BOOM! Along comes a Big Bang.

The big bang theory is the claim that the large-scale behavior of the universe is described by a solution with an intial singularity. All events have time coordinates t>0 in those solutions. There's no t=0 in them. So the big bang wasn't an event in spacetime, it's just a name for the limit t→0.

Now we are 13 billion years down stream and point A is 13 billion lightyears from S (although we never know what S is), and point B is 13 billion light years from point S the other way. A and B are still only 13 billion light years apart. You can't go through S to get from A to B because that would be bigger than 13 billlion light years hence, point S, A and B are on a great circle each 13 billion years from each other. There must be a fourth dimension to create this monstrosity.

In order to determine how far apart they are now, you need to specify how far apart they were at some early time t>0, and what their coordinate velocities were back then. Even if they were very close back then, and both had zero coordinate velocity, they could be unimaginably far apart now (much more than 13.7 billion light-years), because of the expansion of the universe.

 

[stevmg]

You're right... t>0 but can be infinitely close to zero (no minimul required... open interval ... you know all that Dedekind BS.

But, if this all happened, say, 13 billion years ago, no way can the universe we are in be greater than 13 billion light years, at least not in these three dimensions.

Who's to say there aren't other universes and who gives a sh-t what the Pope says that you can't discuss what occurred before t = 0. What the hell does he know about physics? At least he (John-Paul II was the pope who said this) had a handle on evolution and he believed it, much to the chagrin of our Christian and Muslim Fundamentalists.

 

[JesseM]

You're right... t>0 but can be infinitely close to zero (no minimul required... open interval ... you know all that Dedekind BS.

But, if this all happened, say, 13 billion years ago, no way can the universe we are in be greater than 13 billion light years, at least not in these three dimensions.

But the Big Bang isn't an explosion from a central point in a preexisting space--the traditional GR models based on the FLRW metric suppose that every point in space (whether space is treated as finite or infinite) was filled with a uniform density of matter at every moment after the Big Bang. Imagine a universe with only two spatial dimensions (like Flatland), and then imagine those two dimensions curved into the surface of a sphere, with every point on the surface containing some matter. Then the Big Bang and the subsequent expansion of the universe could be thought of in terms of the sphere itself expanding from zero radius, with 2D matter evenly distributed on the surface at all times. Bump up the number of dimensions by 1 and you have something like the model of a Big Bang in a closed universe (for an open universe with infinite size, you can imagine something like an infinite chessboard where all the squares are growing simultaneously, but the amount of matter on each square stays constant so the density is continuously decreasing)

 

[Ich]

Hi Fredrik, JesseM,

as I read it, stevmg is talking about SR only. SR doesn't know cosmological coordinates and the FRW model.
So one could say: SR is not applicable to cosmology, and that's ok.
But, I think, to answer his SR questions, it's ok to neglect gravity and do the cosmology of an empty spacetime in SR coordinates. There, the Big Bang is an explosion, and things are moving away from that explosion with different speeds. That whole model is quite contrived, but it works well enough. So I'm discussing that special explosion, not actual cosmology.

Hi stevmg,

Imagine a point S at the theoretical beginning of time. Then BOOM! Along comes a Big Bang. Say point A flies out to the right at light speed, c.

S is an event, not a point. If you're familiar with spacetime diagrams, you know the difference. If not, I think you best start studying them before doing cosmology.

Also, Point B flies to the left at light speed c. Now, what is the separation speed of points A and B?

Guess what! It is still c.

Ok, but better stay below c. If it were c exactly, there'd be no reference frame of A or B to support such a statement.

Now we are 13 billion years down stream and point A is 13 billion lightyears from S (although we never know what S is), and point B is 13 billion light years from point S the other way.

No. S is not a point, it's an event in the common past of A and B. There is no such thing as a distance A-S or B-S.
If you imagine a point M such that A and B are moving away from it with equal but opposite v<c: There'd be a time when, in M's frame, the distance to A and to B is 13 Gly. At that time, A is 26 Gly away from B - again in M's frame.
At that time, A and B are, say, 10 My old. And they will measure their relative distance to be a tad less than 10 Gly, and their distance to M to be even less.

It's just when you try to calculate in a fram at light speed when it all becomes really weird. That's because such frames don't exist.

what the Pope says that you can't discuss what occurred before t = 0

I don't remember the Pope saying that.

 

[escogido]

I'm not sure if my answer would fall under this category. I want to introduce an idea of transmitting information at a speed faster than the speed of light. I am sure somebody has already thought of this...? Basically all you need is a rod which would exceed the distance of the speed that the light travels, say in an hour (just for practical applications). Pushing that rod at one end will result in the rod being moved at the other end instantly, with zero delay. A principal of a Morse code can be applied - a rod can be pushing a button on the other end, thus transmitting information at a speed faster than the speed of light. Obviously there can be a number of problems with this - the rod can simply be pulled by a gravity of a passing planet, or be hit by a meteorite, etc... But the fact of the matter is that, information can be transmitted at a speed greater than the speed of light.

 

[Dale]

No, it can't. Pushing on a rod transmits information at the speed of sound in that material, which is always much less than the speed of light. And yes, your idea has been thought of many many many times on this forum already.

 

[JesseM]

I'm not sure if my answer would fall under this category. I want to introduce an idea of transmitting information at a speed faster than the speed of light. I am sure somebody has already thought of this...? Basically all you need is a rod which would exceed the distance of the speed that the light travels, say in an hour (just for practical applications). Pushing that rod at one end will result in the rod being moved at the other end instantly, with zero delay. A principal of a Morse code can be applied - a rod can be pushing a button on the other end, thus transmitting information at a speed faster than the speed of light. Obviously there can be a number of problems with this - the rod can simply be pulled by a gravity of a passing planet, or be hit by a meteorite, etc... But the fact of the matter is that, information can be transmitted at a speed greater than the speed of light.

Turns out this idea doesn't work because there are no perfectly rigid objects in relativity (solid objects are just collections of atoms held together be the electromagnetic force, and electromagnetic interactions travel at light speed). If you push one end, it creates a compression wave that travels along the rod at the speed of sound in the material, the other end doesn't move until the wave reaches it. See here for more info:

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#4