I Why is there a universal speed limit, c, and why is it what it is?

[Dmitry67]

if we are in agreement, then I don't understand, why you keep asking about the "ratio".
There is no "ratio" and the situation with "c" is much simpler then with pi.

Unless we for some weird reason measure width in kilometers and height in miles, the "ratio" between width and height is 1 because both are distances in space.

c=1 for the very same reason

 

[SeventhSigma]

OK, maybe this will clarify things if I explain in in this way: We know pi is dimensionless because it involves a mathematical operation between two figures that are given in the same dimensions. Say, a circumference in inches and a diameter in inches. They cancel out to form a dimensionless quantity. This will be the same regardless of the units we use assuming we are referring to the number in the same numeric base (in this case, decimal).

My argument is that c is likely another such "piece of a separate puzzle." It's like knowing the diameter of a circle without knowing the circumference because we don't yet understand the nature of the circle yet. I am saying that it is possible that c, as we know it, is what it is because of some other constraint(s) in our universe.

Clearly we would agree c is not infinite. The question is why this is so.

 

[sahil_time]

c=1/sq.root(epsilon zero*permeability of free space)
Since both are constants hence c is constant!

 

[SeventhSigma]

that's from Maxwell's equations -- epsilon and permeability are derived experimentally -- it is another way to get c but it doesn't explain why it is c.

 

[Dmitry67]

Clearly we would agree c is not infinite. The question is why this is so.

There are 2 separate questions;

1. Why there is "c" at all. This is because our space is not euclidean, but pseudoeuclidean with metrics (+++-). You can ask "why", it is like asking "why we have these particular physical laws"

2. The question about the particular value of "c". We discussed it before. There are no puzzles. Distance in space is defined as

s^2 = x^2 + y^2 + ...

not as

s^2 = x^2 + 1.3 y^2 + ...

nor

s^2 = x^2 + 0.9 y^2 + ...

as different directions in space are measured in the same units, c must be =1 and can't be different.

P.S.
Note: if scientists from the very beginning would have used Planks (natural) units, all formulas will be different: there won't be "c", "G" and "h" at all!

 

[Tanelorn]

I understand that beyond the edge of the observable universe galaxies are traveling well beyond the speed of light away from us relative to us, as is the light they emit. Further, when the CMBR that we see today was first emitted, it was traveling at over 500 times the speed of light away from us (but traveling towards us) and has only just had chance to reach us. Thought that would cheer you up :)

 

[SeventhSigma]

1. Yes, the question is like asking "why do we have these particular physical laws."

2. Yes, we can define c as 1 if we want to use it as a natural unit. This is an example of "labeling" as I define it, and this is not what I am discussing. We don't answer the question by just relabeling something as a fundamental unit of 1 because then we could just ask "Why is everything so slow in comparison?" and it brings us to the same problem.

 

[Tanelorn]

c=1/sq.root(epsilon zero*permeability of free space)
Since both are constants hence c is constant!

Permitivity and permeability are not constants of nature, They're artifacts of a particular choice of electromagnetic units (SI). In Gaussian CGS and Heaviside-Lorentz CGS units, they don't exist.

 

[Dmitry67]

1. Yes, the question is like asking "why do we have these particular physical laws."

2. because then we could just ask "Why is everything so slow in comparison?" and it brings us to the same problem.

1. We don't know. But if space was simply Euclidean, there would be no "time"

2. Pseudo-Euclidean structure of space-time itself does not limit speeds to <1, for example, hypothetical tachyons can move faster than light. However, because of the way how we interpret space and time, something moving faster than light is interpreted as “spacelike”, something that has spatial extent.

 

[nitsuj]

It's a cap in the sense that if we define a meter in an arbitrary way and time in an arbitrary way, we can therefore define speed in an arbitrary way. The speed of light is not infinite and therefore there is an upper bound to it that we can describe with our arbitrary definitions of speed. Again, the question is not about labels but the relative ratios.

Coincidently the "speed of light"/"c" is not speed at all, (again you taught me that) but the point that time stops. If time stopped at 200,000km/s then I am guessing it would be impossible for something to go faster since time stops.

Don't blame the limit on speed, blame it on time(distance/space).

 

[Dmitry67]

Coincidently the "speed of light"/"c" is not speed at all, (again you taught me that) but the point that time stops. If time stopped at 200,000km/s then I am guessing it would be impossible for something to go faster since time stops.

time does not stop because it does not move.
just the interval and proper time becomes 0 at v=c.
and it has nothing to do with an ability to move FTL: tachyons always move FTL, and they can't slow down to c (even they probably don't exist for the other reasons)

 

[nitsuj]

Clearly we would agree c is not infinite.

c IS infinite in every sense of the word. I feel as if c defines infinite. maybe the idea of 300,000 distance of some kind with a "time" of some kind, is a misnomer when thought of in the context of "c", because there is no time at 300,000 km/s.

excerpt from Brian greene's The Elegant Universe pg52

"So as a moun moves more quickly it gets ever more difficult to increase its speed. At 99.999 percent of the speed of light the mass of a moun has increased by a factor of 224; at 99.99999999 percent of the speed of light it has increased by a factor of more than 70,000. Since the mass of the muon increases without limit as it's speed approaches that of light, it would require a push with an infinite amount of energy to reach or cross the light barrier."

 

[nitsuj]

time does not stop because it does not move.
just the interval and proper time becomes 0 at v=c.
and it has nothing to do with an ability to move FTL: tachyons always move FTL, and they can't slow down to c (even they probably don't exist for the other reasons)

I can't define time as anything else but movement. I see time as a "consequence" of movement in space. Said differently, Derived from movement in space. So much so that "the interval and proper time becomes 0 at v=c", whatever that means, just looks like the math agrees.

"(even they probably don't exist for the other reasons)" seems like weaker support than "...time becomes 0 at v=c"


From wikipedia
A tachyon- is a hypothetical subatomic particle that moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds.

"Imaginary time is obtained from real time via a Wick rotation..."


This hardly seems fair as a point of arguement.

 

[bobc2]

I would tend to study the significance of the constant speed, c, for all observers by considering the 4th dimension a spatial dimension--not a time dimension at all. Proper time along any observer's 4th dimension is merely a parameter. The understanding of time itself necessarily involves an understanding of consciousness, neurology and psychology. For example you can carry a clock with you as you drive up the interstate at a constant speed of 70 mph and assign time values to every mile along the way--but that in no way makes that highway anything but a spatial dimension. Every observer is moving along his own 4th dimension at the speed of light--just like driving up the interstate--you can record proper time values along the 4th dimension trip, but that in no way makes X4 anything but a spatial dimension.

So, the essence of what's behind the constant value of "light speed" implies an understanding of the universe as a 4-dimensional structure (the so-called "block universe") populated by 4-dimensional objects (the photon being modeled below as a 4-dimensional world line). You see the "speed" in this case is really shown as the ratio of distances (X1/X4), i.e., literally a dimensionless quantity. And that ratio is of course: 1.000----. simply because the world line of the photon bisects the angle between X1 and X4 for all observers, regardless of speed.

The other question as to why there is a limiting factor can be seen in the sequence of diagrams showing increasing observer speeds (blue coordinates) with respect to the black coordinates. The key here is nature's strange characteristic of rotating the X1 axis to maintain symmetry about the photon world line for increasing rotations of the X4 axis. You can plainly see that the X1 axis merges with the X4 axis in the limit. I think this is this "limiting" condition is what you may be trying to graple with. The fundamental question is "Why does nature rotate the X1 axis like this?" (The rotations are described mathematically by Lorentz transformations).

Of course, bcrowell had it right when he advised us to first choose the postulates. I have not formalized my statements of postulates well.

 

[Dale]

c IS infinite in every sense of the word.

No way. C is finite. It is not infinite in any sense of the word.

 

[DrGreg]

c IS infinite in every sense of the word.

If you had said "c behaves a bit like infinity in some senses" you might have a point. To say "c is infinite in every sense" is complete nonsense. Do you really think the "equation"

299792458 = \infty​

makes any sense at all?

 

[nitsuj]

If you had said "c behaves a bit like infinity in some senses" you might have a point. To say "c is infinite in every sense" is complete nonsense. Do you really think the "equation"

299792458 = \infty​

makes any sense at all?

Can you explain what I would have meant if I had said "c behaves...". Does it show "behaviour" in graphs and equations?

299792458 = c = no time = no movement = infinity = ? as in the graph above
is infinity actualy used in math?

 

[Dale]

299792458 = c = no time = no movement = infinity

Absurd. c does not equal "no time". What you mean is that:
\lim_{v\to c} \, \gamma(v)=\infty

That certainly is not the same as c being either infinite or equal to "no time".

 

[nitsuj]

No way. C is finite. It is not infinite in any sense of the word.

yea? ask the one traveling at C, their reply might take what seems like an infinitly long time.

 

[Dmitry67]

1
I can't define time as anything else but movement. I see time as a "consequence" of movement in space. Said differently, Derived from movement in space. So much so that "the interval and proper time becomes 0 at v=c", whatever that means, just looks like the math agrees.


2
"Imaginary time is obtained from real time via a Wick rotation..."
This hardly seems fair as a point of arguement.

1 Well, it is a definition based on our "common sense"
The key finding of GR is taht time is a a 4th dimention, not "rate of change of things" or other wordy stuff usually used by the philosophers.

2 And what? (forget that they probably don't exist for now)
Tachyons always move faster than c, so for then c is also a barrier, but a LOW limit of seed - it requires for them an infinite amount of energy to slow down to c.

 

[Dale]

yea? ask the one traveling at C, their reply might take what seems like an infinitly long time.

That doesn't mean that c is infininte, it means that time dilation is infinite at c (more precisely the limit stated above). That c is finite is one of the key facts of relativity.

 

[Huttate]

So we have photons that travel at a speed that we ascertain to be the maximum possible speed in our universe. But for them, although we are not allowed to think of their frame of reference [it is meaningless] time has no meaning and is not experienced. Any attempt to attribute a half-life to them renders an infinite.

Trying to attain their view of the universe is therefore impossible.

These photons are the gauge bosons of interractions that create and destroy atomic structures and therefore everything we know in the physical world, including ourselves.

The mind boggles to think that those photons which constitute the CMB have themselves experienced no passage of time.

Is all this right so far?

We have something that is ageless, stretches effortlessly across time as we see it and is [responsible] for the creation of all matter and life.

I'm an atheist but were I not I think I could add another level of spin to the photon.

Let there be light!

 

[nitsuj]

That doesn't mean that c is infininte, it means that time dilation is infinite at c (more precisely the limit stated above). That c is finite is one of the key facts of relativity.

Ah okay,

I thought that I was talking about time being infinite at "c",

I also thought that because "c" is finite to an observer that it is measurable, but that if traveling at "c" it would not be, and that this oddity was one of the facts of special relativity.
Seems I am greatly mistaken, back to the beginning for me.

 

[SeventhSigma]

Ah okay,

I thought that I was talking about time being infinite at "c",

I also thought that because "c" is finite to an observer that it is measurable, but that if traveling at "c" it would not be, and that this oddity was one of the facts of special relativity.

Seems I am greatly mistaken, back to the beginning for me.

The point of special relativity relies on the notion that c is the same for all observers. You can derive tile dilation from, for example, the famous light-clock diagram.

Ultimately we find t=T*(1-v^2/c^2)^.5 or T*gamma. As v approaches c, gamma approaches 0. So hypothetically, at v=c we have T*gamma = T*0 = 0 = t, which implies that no matter how much time passes for T (the clock according to the observer moving at c), we'll see t's clock frozen in time.

 

[nitsuj]

1 Well, it is a definition based on our "common sense"
The key finding of GR is taht time is a a 4th dimention, not "rate of change of things" or other wordy stuff usually used by the philosophers.

2 And what? (forget that they probably don't exist for now)
Tachyons always move faster than c, so for then c is also a barrier, but a LOW limit of seed - it requires for them an infinite amount of energy to slow down to c.

1. Is "time in SR, different to "time" in GR?
Dmitry67 I am trying to understand what time is and the best I can come up with is movement in space. "rate of change" is simular enough to how I think of it. Why is that wrong in SR? (keep it simple please or I'll be lost in a few words)

2. I can't even come up with a reply to this. Seems like a different subject then SR, and something I never read or thought of ( outside of they may not be real, are based on Imaginary Real Time - all things outside my understanding, next to SR apparently)

 

[Dmitry67]

SR is a particular case of GR, GR in flat spacetime.
I suggest checking this link:
http://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time)
It explains what is time (based on SR and GR)

 

[nitsuj]

The point of special relativity relies on the notion that c is the same for all observers. You can derive tile dilation from, for example, the famous light-clock diagram.

Ultimately we find t=T*(1-v^2/c^2)^.5 or T*gamma. As v approaches c, gamma approaches 0. So hypothetically, at v=c we have T*gamma = T*0 = 0 = t, which implies that no matter how much time passes for T (the clock according to the observer moving at c), we'll see t's clock frozen in time.

Sorry for the time, but I don't understand equations beyond + - * / = and in that order :) and that's a part of my misunderstanding i'd guess.
I think I got the part that "c" is the same for everyone.

I guess I take the "time stops at "c" too far when I think of someone in a ship traveling at "c" that there is no time passing (and in turn no movement, rulers shrink to nothing ect) being the same as infinity.

 

[bcrowell]

The fundamental question is "Why does nature rotate the X1 axis like this?" (The rotations are described mathematically by Lorentz transformations).
[...]
Of course, bcrowell had it right when he advised us to first choose the postulates. I have not formalized my statements of postulates well.

I would say that if you take postulates P1+P2 from #3, then x1 has to rotate because the transformation has to be linear (due to the homogeneity of space) and has to leave the x1=x4 diagonal fixed (due to P2).

If you prefer (as I do) the symmetry-based postulates in the systems referenced in #3, then there are three cases, in which x1 rotates clockwise, counterclockwise, or not at all. The counterclockwise case violates causality. The nonrotating case is Galilean relativity. You need a postulate to say that you want the clockwise case rather than the nonrotating one; this postulate is strongly motivated because we observe that time is not absolute, e.g., in the Hafele-Keating experiment. Given that postulate, you can then prove as a theorem that there is some velocity that is the same for all observers (because if x1 rotates clockwise and x4 counterclockwise, and the transformation is linear, there must be some line that doesn't rotate at all).

 

[Quickless]

1. e = mc(squared) - c(squared) is the rate at which matter is transformed into energy.

2. What constrains c - c is a function of the electric and magnetic fields - Maxwell

3. For c a. velocity is constant b. acceleration is equal to zero (This is more interesting than the value of c).


a. It was never established ex ante that a = o for c. It was just assumed.
b. It is very convenient to have a=0 for c. Lots of equations just disappear.
c. The constant velocity of c with respect to all regimes both real and imagined suggests that the wave/particle conception is flawed. Constant velocity pertains more to the properties of a field than a wave/particle.

I just made all this up but I had fun.

Q

 

[bobc2]

I would say that if you take postulates P1+P2 from #3, then x1 has to rotate because the transformation has to be linear (due to the homogeneity of space) and has to leave the x1=x4 diagonal fixed (due to P2).

If you prefer (as I do) the symmetry-based postulates in the systems referenced in #3, then there are three cases, in which x1 rotates clockwise, counterclockwise, or not at all. The counterclockwise case violates causality. The nonrotating case is Galilean relativity. You need a postulate to say that you want the clockwise case rather than the nonrotating one; this postulate is strongly motivated because we observe that time is not absolute, e.g., in the Hafele-Keating experiment. Given that postulate, you can then prove as a theorem that there is some velocity that is the same for all observers (because if x1 rotates clockwise and x4 counterclockwise, and the transformation is linear, there must be some line that doesn't rotate at all).

Good job as usual, bcrowell. Thanks.