Speeds greater than the speed of light

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The discussion centers on the possibility of speeds greater than the speed of light and their implications for relativity. It asserts that while theoretical calculations suggest superluminal speeds, none can be achieved by objects with mass, and the universal constant 'c' cannot be discarded. Superluminal communication raises paradoxes, such as the violation of causality and the potential for signaling backwards in time, which contradicts established principles of physics. Participants argue that accepting superluminal speeds would necessitate rejecting fundamental concepts like the precedence of cause over effect and the uniformity of physical laws across reference frames. Ultimately, the consensus is that superluminal communication remains a speculative idea that challenges the foundations of current physical theories.
  • #61
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.
 
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  • #62
first:

HallsofIvy said:
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..

Mr.Amin said:
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.
 
  • #63
HallsofIvy said:
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.
 
  • #64
carstenk said:
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.
 
  • #65
carstenk said:
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.
carstenk said:
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).
 
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  • #66
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.
 
  • #67
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"
 
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  • #68
cyberfish99 said:
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.
 
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  • #69
JesseM said:
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.
 
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  • #70
carstenk said:
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

carstenk said:
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 .
 
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  • #71
JesseM said:
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.
 
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  • #72
cfrogue said:
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').
 
  • #73
JesseM said:
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.
 
  • #74
cfrogue said:
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)
 
  • #75
JesseM said:
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".
 
  • #76
cfrogue said:
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).
 
  • #77
JesseM said:
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.
 
  • #78
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
 
  • #79
Mihael@@/& said:
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.
 
  • #80
And how many ours have you thought about that? Or who proved it? Let's sacrifice him:)
 
  • #81
Mihael@@/& said:
Or who proved it?
I believe it was either Einstein or Minkowski, but I don't have a reference.
 
  • #82
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.
 
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  • #83
heldervelez said:
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.
 
  • #84
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?
 
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  • #85
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.
 
  • #86
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...
 
  • #87
stevmg said:
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.

stevmg said:
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.
 
  • #88
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.
 
  • #89
stevmg said:
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)
 
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  • #90
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.
 

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