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

[CosmicVoyager]

Greetings,

Why is there a c? Why is there a speed limit to the universe? Why is there a limit to how quickly a cause can follow an effect at distance? Why is there a "causality constant"?

What is(are) the limiting factor(s) that make it what is? The speed limit is a consequence of what? Is what we know to be the speed limit the result of measurements? Or is it a logical problem that can be figured out in a thought experiment?

What was God thinking? lol

Thanks

 

[bobc2]

Greetings,

The reason I asked that question https://www.physicsforums.com/showthread.php?p=3174840 was so that I could ask this question properly.

Why is there a c? Why is there a speed limit to the universe? Why is there a limit to how quickly a cause can follow an effect at distance? Why is there a "causality constant"?

What is(are) the limiting factor(s) that make it what is? The speed limit is a consequence of what? Is what we know to be the speed limit the result of measurements? Or is it a logical problem that can be figured out in a thought experiment?

What was God thinking? lol

Thanks

Of course I do not know the answer to your question. However, you might be interested in considering the following. Perhaps nature decided to manifest its physics on a R4 manifold with a 4-dimensional space populated with 4-D observers. Observers could take the form of objects with relatively long world lines (relatively short 3-D lengths) oriented in various ways. Affine coordinates were selected as a background for the natural positioning of the 4-D objects in patterns that would manifest physics. That is, the same physics would be manifest to all observers, regardless of the orientation of the world lines.

There are world lines for inanimate 4-D objects and worldlines for 4-D observers. However, the world lines, extending along the X4 axis of a given object, would be oriented with angles that would not exceed 45 degrees. Along with this, observers experience the phenomena of time--the observer (in some sense) moves along his world line at the speed, c. And any observer, at any instant of time, would "live in" a 3-D cross section of the 4-D universe at the corresponding point along his world line. Further, that view would be along X1 of his affine coordinates (X2 and X3 are suppressed in this example).

In the sequence of views below, different observer world lines are shown, corresponding to increasing velocities with respect to a rest frame. The X1 axis always rotates to an angle symmetric with the X4 relative to the 45 degree world line. You see that if the world line of an observer rotated 45 degrees clockwise, then the X1 would rotate 45 degrees counter clockwise, and the X4 and X1 would then be colinear. That would represent some kind of physical boundary--the observer would not be able to make any sense of such a 3-D cross-section view of the manifold. Correspondingly, the physics is designed to avoid this colinear result for observers.

Of course that 45 degree world line is a 4-dimensional photon, having the velocity, c. Thus, the speed of light, in this fanciful description of 4-dimensional space inhabited by 4-D observers, is a natural consequence of an affine space designed for 4-D observers who must experience the same physics, regarless of their world line orientation. Accordingly, all observers will obtain the same value, 186,000 mi/sec, when measuring the speed of light, regardless of an observer's speed.

 

[bcrowell]

The answer to a "why" question like this can depend on what you take to be an unprovable postulate. The following FAQ entry is aimed at a slightly different question, which is why c is frame-invariant. However, once you believe in a frame-invariant speed, it's pretty hard to escape the conclusion that that speed is also the speed limit on cause and effect. As for the reason c has the numerical value it has, the reason is that we defined a system of units in which it has that value. Relativists often find it more convenient to work in a system where c=1.

FAQ: Why is the speed of light the same in all frames of reference?

The first thing to worry about here is that when you ask someone for a satisfying answer to a "why" question, you have to define what you think would be satisfying. If you ask Euclid why the Pythagorean theorem is true, he'll show you a proof based on his five postulates. But it's also possible to form a logically equivalent system by replacing his parallel postulate with one that asserts the Pythagorean theorem to be true; in this case, we would say that the reason the "parallel theorem" is true is that we can prove it based on the "Pythagorean postulate."

Einstein's original 1905 postulates for special relativity went like this:

P1 - "The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion."

P2 - "Any ray of light moves in the 'stationary' system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body."

From the modern point of view, it was a mistake for Einstein to single out light for special treatment, and we imagine that the mistake was made because in 1905 the electromagnetic field was the only known fundamental field. Really, relativity is about space and time, not light. We could therefore replace P2 with:

P2* - "There exists a velocity c such that when something has that velocity, all observers agree on it."

And finally, there are completely different systems of axioms that are logically equivalent to Einstein's, and that do not take the frame-independence of c as a postulate (Ignatowsky 1911, Rindler 1979, Pal 2003). These systems take the symmetry properties of spacetime as their basic assumptions.

For someone who likes axioms P1+P2, the frame-independence of the speed of light is a postulate, so it can't be proved. The reason we pick it as a postulate is that it appears to be true based on observations such as the Michelson-Morley experiment.

If we prefer P1+P2* instead, then we actually don't know whether the speed of light is frame-independent. What we do know is that the empirical upper bound on the mass of the photon is extremely small (Lakes 1998), and we can prove that massless particles must move at the universal velocity c.

In the symmetry-based systems, the existence of a universal velocity c is proved rather than assumed, and the behavior of photons is related empirically to c in the same way as for P1+P2*. We then have a satisfying answer to the "why" question, which is that existence of a universal speed c is a property of spacetime that must exist because spacetime has certain other properties.

W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

Palash B. Pal, "Nothing but Relativity," http://arxiv.org/abs/physics/0302045v1

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

 

[CosmicVoyager]

We can prove that massless particles must move at the universal velocity c.

In the symmetry-based systems, the existence of a universal velocity c is proved rather than assumed, and the behavior of photons is related empirically to c in the same way as for P1+P2*. We then have a satisfying answer to the "why" question, which is that existence of a universal speed c is a property of spacetime that must exist because spacetime has certain other properties.

I am asking why there is a "universal velocity c."

Why is there a c? Why is there a speed limit to the universe? Why is there a limit to how quickly a cause can follow an effect at distance? Why is there a "causality constant"?

What is(are) the limiting factor(s) that make it what is? The speed limit is a consequence of what? Is what we know to be the speed limit the result of measurements? Or is it a logical problem that can be figured out in a thought experiment?

 

[CosmicVoyager]

Of course I do not know the answer to your question. However, you might be interested in considering the following. Perhaps nature decided to manifest its physics on a R4 manifold with a 4-dimensional space populated with 4-D observers. Observers could take the form of objects with relatively long world lines (relatively short 3-D lengths) oriented in various ways. Affine coordinates were selected as a background for the natural positioning of the 4-D objects in patterns that would manifest physics. That is, the same physics would be manifest to all observers, regardless of the orientation of the world lines.

There are world lines for inanimate 4-D objects and worldlines for 4-D observers. However, the world lines, extending along the X4 axis of a given object, would be oriented with angles that would not exceed 45 degrees. Along with this, observers experience the phenomena of time--the observer (in some sense) moves along his world line at the speed, c. And any observer, at any instant of time, would "live in" a 3-D cross section of the 4-D universe at the corresponding point along his world line. Further, that view would be along X1 of his affine coordinates (X2 and X3 are suppressed in this example).

In the sequence of views below, different observer world lines are shown, corresponding to increasing velocities with respect to a rest frame. The X1 axis always rotates to an angle symmetric with the X4 relative to the 45 degree world line. You see that if the world line of an observer rotated 45 degrees clockwise, then the X1 would rotate 45 degrees counter clockwise, and the X4 and X1 would then be colinear. That would represent some kind of physical boundary--the observer would not be able to make any sense of such a 3-D cross-section view of the manifold. Correspondingly, the physics is designed to avoid this colinear result for observers.

Of course that 45 degree world line is a 4-dimensional photon, having the velocity, c. Thus, the speed of light, in this fanciful description of 4-dimensional space inhabited by 4-D observers, is a natural consequence of an affine space designed for 4-D observers who must experience the same physics, regarless of their world line orientation. Accordingly, all observers will obtain the same value, 186,000 mi/sec, when measuring the speed of light, regardless of an observer's speed.

Thank you for your answer, but I don't understand it :-( One reason is the terminology. I am very good at explaining anything to anyone. It is a rare talent I have. But first I need to understand it. I am hoping somone can explain it to me closer to the way I would. Not assuming one knows what manifolds and world lines are. To break it down step by step. Illustrations would help/ I don't understand the one above.

I will try to read this more times and see if I can translate it.

 

[bobc2]

Thank you for your answer, but I don't understand it :-( One reason is the terminology. I am very good at explaining anything to anyone. It is a rare talent I have. But first I need to understand it. I am hoping somone can explain it to me closer to the way I would. Not assuming one knows what manifolds and world lines are. To break it down step by step. Illustrations would help/ I don't understand the one above.

I will try to read this more times and see if I can translate it.

I think the spacetime diagrams with the world lines might be a way for you to grasp some fundamental concepts. I realized that you might not understand the diagrams at all, but I didn't really know your background well enough to judge. It was a description that I hoped would not get too detailed and lengthy.

I can walk you through the understanding of the spacetime diagrams if you wish to pursue things in that kind of detail. And there are others on the forum here who are better than I at explaining things.

 

[CosmicVoyager]

Thank you for your answer, but I don't understand it :-( One reason is the terminology. I am very good at explaining anything to anyone. It is a rare talent I have. But first I need to understand it. I am hoping somone can explain it to me closer to the way I would. Not assuming one knows what manifolds and world lines are. To break it down step by step. Illustrations would help/ I don't understand the one above.

I will try to read this more times and see if I can translate it.

Regarding th diagram, what are X1, X2, X3, and X4? Is X4 the observer? Why does it also say X4 is time? I can't make out what is at the end of the black lines. It this a 2D graph? What does it mean by the blue axes rotate?

"The blue X4 and X1 axes would appear to converge on themselves, becoming colinear, in the limit as the observer's speed approaches light speed."

Huh? LOL "in the limit"? "appear to converge"? What does how something appear have to do with how fast things can travel?

 

[CosmicVoyager]

Greetings,

Here are examples of what a conceptual explanation as to why there is a universal speed limit would be like, if they were true :-)

Ideas:

- Everything in the universe is moving through a medium. The medium causes resistance. The faster something goes the greater the resistance is. The resistance increases exponentially similar to air resistance increasing on a car.

- Time and space are made up of indivisible units. The fastest possible speed is one space unit per unit of time, otherwise things would be skipping over points in space.

Does anyone know the answer and able to explain it?

Thanks

 

[Pengwuino]

I am asking why there is a "universal velocity c."

Why is there a c? Why is there a speed limit to the universe? Why is there a limit to how quickly a cause can follow an effect at distance? Why is there a "causality constant"?

What is(are) the limiting factor(s) that make it what is? The speed limit is a consequence of what? Is what we know to be the speed limit the result of measurements? Or is it a logical problem that can be figured out in a thought experiment?

Because God said so.

Really, there is no answer to this question. We OBSERVE the universal speed limit of the speed of light. However, WHY this is the case is impossible to answer. If there were no speed limit, you could formulate a universe that works perfectly well. It would be different than what we see in our limited-speed universe, but that universe would probably think "hmm, why is there no speed limit?". It just is what it is. Any explanation you would get is not an answer to your question, it's just a way of explaining what the world is like BECAUSE there is a universal speed limit, not what brought about it in the first place.

 

[CosmicVoyager]

Because God said so.

Really, there is no answer to this question. We OBSERVE the universal speed limit of the speed of light. However, WHY this is the case is impossible to answer. If there were no speed limit, you could formulate a universe that works perfectly well. It would be different than what we see in our limited-speed universe, but that universe would probably think "hmm, why is there no speed limit?". It just is what it is. Any explanation you would get is not an answer to your question, it's just a way of explaining what the world is like BECAUSE there is a universal speed limit, not what brought about it in the first place.

There is an answer. It's just no one has thought of it yet :-)

"but that universe would probably think "hmm, why is there no speed limit?""

No, if they know of nothing to limit the speed, there is no reason to think there should be a limit.

Right now, I don't know of anything to restrict speed, other than the total energy available to accelerate something."Any explanation you would get is not an answer to your question"

Yes it would, like the two examples answers I gave.

What is it that is restricting the speed?

I think the Lorentz post by bcrowell might explain it, but I do not understand it.

 

[Radu094]

Well, like bcrowell was saying, when asking 'why' questions, you inevitably end-up with a sequence like: Why is 'A' true? Because 'B' is true. Well, then why is 'B' true? Because 'C' is true. Well, then why is 'C' true? ... and you can do this for a long time until the answer comes back as either "Because 'A' is true" or "Because we have observed it in an experiment, and we know Z to be true".

Either way, you need to pick one of the answers in that chain and accept it to be true apriori based on experiments and observations (this will be your postulate).

Now you can directly accept P2* as a postulate (ie. we know there is a speed limit because we have observed it) and then, well, that will be your answer. It's the physics equivalent of "Because I said so ! "

If you want to dig deeper ,you can ignore P2*, assume other postulates to be true, look into other physics postulates (causality, gravity) and then from those experiments you can infer that there MUST be a universal speed limit. In this case your answer will be " there is a speed limit as a property of the universe, because other properties of the universe (properties that we have observed and measure and know to be true) require a speed limit".

Either way you are not better off,really.

'c' as a speed limit is a property of our universe that makes it behave like it does. Changing this speed limit's value (or removing it), much like changing any other property of the universe, would result in a totally different universe where many of the things we are accustomed to might not exist: cause and effect, differences between past an present, time flowing in a single direction.

Did I get it right, bcrowell ?

 

[CosmicVoyager]

Well, like bcrowell was saying, when asking 'why' questions, you inevitably end-up with a sequence like: Why is 'A' true? Because 'B' is true. Well, then why is 'B' true? Because 'C' is true. Well, then why is 'C' true? ... and you can do this for a long time until the answer comes back as either "Because 'A' is true" or "Because we have observed it in an experiment, and we know Z to be true".

Either way, you need to pick one of the answers in that chain and accept it to be true apriori based on experiments and observations (this will be your postulate).

Now you can directly accept P2* as a postulate (ie. we know there is a speed limit because we have observed it) and then, well, that will be your answer. It's the physics equivalent of "Because I said so ! "

If you want to dig deeper ,you can ignore P2*, assume other postulates to be true, look into other physics postulates (causality, gravity) and then from those experiments you can infer that there MUST be a universal speed limit. In this case your answer will be " there is a speed limit as a property of the universe, because other properties of the universe (properties that we have observed and measure and know to be true) require a speed limit".

Either way you are not better off,really.

'c' as a speed limit is a property of our universe that makes it behave like it does. Changing this speed limit's value (or removing it), much like changing any other property of the universe, would result in a totally different universe where many of the things we are accustomed to might not exist: cause and effect, differences between past an present, time flowing in a single direction.

Did I get it right, bcrowell ?

I am extremely confident that I will understand with there is a speed limit, and when I do I will be able to explain it in a few sentences. And I will ask why someone else who understood couldn't have done that. I know because it keeps happening. There is an explanation for why there must be a limit and why it is what it is.

 

[CosmicVoyager]

From another thread:

A better understanding of c, is not so much as the speed limit but as a unit conversion factor. The E=mc^2 equation is an identity "mass is energy" plus a unit conversion.
1kg = c^2 joules.

In that context, also note that "speed" is just a slope in space-time and unitless when working in common units. I find this helps to understand the "speed limit" as a geometric phenomenon instead of a dynamic one.

This is excellent. I think this is headed in the right direction. Conceptually, the important form of the equation e=mc^2 is c=squarroot(m/e). The real question is why is the speed limit of the universe equal to the square root of the mass of any object divided by it's energy. I get the feeling that it must be, by the very definitions of what mass and energy are. I don't see it yet though. I think this is very close. Something to do with the fact that energy is motion. I will think about it. If anyone can illustrate why that must be so, please do.

The square root of mass divided by energy. Hmm...

 

[bcrowell]

I am asking why there is a "universal velocity c."

Why is there a c? Why is there a speed limit to the universe? Why is there a limit to how quickly a cause can follow an effect at distance? Why is there a "causality constant"?

As explained in #3, the answer to this sort of question depends on what you want to use as postulates. Spell out your postulates for us, and then people can take a crack at answering your question.

 

[Forestman]

Maybe if chaotic inflationary cosmology is right, and there is a multiverse, with each universe having different values for all the constants and forces, perhaps the speed of light came to be like it is merely by chance. In some other universe it might be faster, or slower, than it is in our universe.

 

[Naty1]

As noted there is no known answer...any more than we know why an electron and proton have the charge we observe...

but is likely due one of the following reasons:

(a) nature "selected" this UNIQUE factor because it's a constant that makes our unique and one time one of a kind of universe (and hence us) possible,

(b) It's one of an infinite number of possible situations among an infinite number of universes..and this one happened to give rise to us...

(c) "God", Allah, Budda, or anoher designer of your choice, picked it...and maybe us, too...

 

[Pengwuino]

There is an answer. It's just no one has thought of it yet :-)

"but that universe would probably think "hmm, why is there no speed limit?""

No, if they know of nothing to limit the speed, there is no reason to think there should be a limit.

Why not? Historically, when we did not know of a speed limit, it was asked why there is no speed limit. Why wouldn't the converse be true?

Right now, I don't know of anything to restrict speed, other than the total energy available to accelerate something.

No, the speed of light is the restriction, even with infinite amounts of energy available.

"Any explanation you would get is not an answer to your question"

Yes it would, like the two examples answers I gave.

What is it that is restricting the speed?

This is getting ot what another poster said. If you use your idea that there are some sort of discrete steps things have to take in space-time or what have you, that model is probably going to be simply a consequence of this speed limit of the universe. Then again, maybe it is the other way around? Who knows, it's the chicken and the egg problem. The speed of light can be your assumption and ideas B, C, D, and E follow from the speed of light. Or you can take idea B, C, D, and E as postulates, and the speed of light being constant will follow from that.

The thing is, most people see the speed of causality as the speed limit and use it as one of the many postulates when constructing theories. So theories never give a "why" to that question, only ideas that follow. You COULD postulate something else completely unrelated to what we know about physics and if by some miracle you came to the conclusion that the speed of light has to be constant (and of course, everything else we already know about physics), but that would be wild to say the least.

 

[bcrowell]

As noted there is no known answer

I disagree. Depending on what you take as your postulates, there can be a known answer. If you choose the postulates used in this paper Palash B. Pal, "Nothing but Relativity," http://arxiv.org/abs/physics/0302045v1
, for example, then the existence of a frame-invariant speed limit is a theorem that can be proved from those postulates.

 

[CosmicVoyager]

As noted there is no known answer...any more than we know why an electron and proton have the charge we observe...

but is likely due one of the following reasons:

(a) nature "selected" this UNIQUE factor because it's a constant that makes our unique and one time one of a kind of universe (and hence us) possible,

(b) It's one of an infinite number of possible situations among an infinite number of universes..and this one happened to give rise to us...

(c) "God", Allah, Budda, or anoher designer of your choice, picked it...and maybe us, too...

I am not asking something like you describe above. I am not asking something like why an electron has the charge is does.

What am asking is the same way I would ask why is there a limit to how much mass an object can have, or why is there a limit to ow big and object can be, or why is there a limit to how fast something can spin? It seems there is not reason there should be limits, ad if there is what is limiting factor? What is causing the restriction?

 

[CosmicVoyager]

Originally Posted by jambaugh View Post

" A better understanding of c, is not so much as the speed limit but as a unit conversion factor. The E=mc^2 equation is an identity "mass is energy" plus a unit conversion.
1kg = c^2 joules.

In that context, also note that "speed" is just a slope in space-time and unitless when working in common units. I find this helps to understand the "speed limit" as a geometric phenomenon instead of a dynamic one."


This is excellent. I think this is headed in the right direction. Conceptually, the important form of the equation e=mc^2 is c=squarroot(m/e). The real question is why is the speed limit of the universe equal to the square root of the mass of any object divided by it's energy. I get the feeling that it must be, by the very definitions of what mass and energy are. I don't see it yet though. I think this is very close. Something to do with the fact that energy is motion. I will think about it. If anyone can illustrate why that must be so, please do.

The square root of mass divided by energy. Hmm...

I hypothesize that it is not a random coincidence that the square root of (m/e) exactly equals the speed limit. I think there is some connection between matter and energy and the speed limit.

 

[harrylin]

I am not asking something like you describe above. I am not asking something like why an electron has the charge is does.

What am asking is the same way I would ask why is there a limit to how much mass an object can have, or why is there a limit to ow big and object can be, or why is there a limit to how fast something can spin? It seems there is not reason there should be limits, ad if there is what is limiting factor? What is causing the restriction?

Another way to look at it is that everything has wave nature (read up on De Broglie, http://en.wikipedia.org/wiki/Matter_wave). Therefore nothing can go faster than the speed of light, just as no sound wave can go faster than the speed of sound.

Note that different people give different answers to that question, and probably nobody can prove to really have the right answer.

Harald

 

[bcrowell]

Another way to look at it is that everything has wave nature (read up on De Broglie, http://en.wikipedia.org/wiki/Matter_wave). Therefore nothing can go faster than the speed of light, just as no sound wave can go faster than the speed of sound.

This argument doesn't make sense. There is no (direct) logical connection between the speed of an electron wave and the speed of a photon wave.

Note that different people give different answers to that question, and probably nobody can prove to really have the right answer.

This is incorrect. Once you fix a set of postulates, there is a right answer. See http://arxiv.org/abs/physics/0302045v1

I hypothesize that it is not a random coincidence that the square root of (m/e) exactly equals the speed limit. I think there is some connection between matter and energy and the speed limit.

See Einstein, "Does the inertia of a body depend upon its energy content?," Annalen der Physik. 18, 639: 1905. English translations are available online.

 

[_PJ_]

My answer here:

https://www.physicsforums.com/showthread.php?t=478783&page=2

in CosmicVoyager's similar thread explains why c defines a limit.

Why c holds the value it does, though, is a different matter entirely. Naturally, the units used are meaningless since metres are derived from the observed speed of light in vacuo and the second relates to Caesium decay. This means that the 2.99897(or whatever) ms^-1 number is not significant as a quantity, but as a unique value, like PI (which is ultimately defined by the curvatre of spacetime), or the the natural logarithm/root, or the fine structure constant, or the universal gravitation, it has a special characteristic of being a constant (to our current understanding, theories of c variance notwithstanding) in our universe.

Regardless of the wavelength of light, how much energy it has, it maintains the constant speed. Unlike massive objects for which the greater their mass, the more energy is needed.
That bosons have a fixed speed, DeBroglie showed how E is related to wavelength as well as mass, giving a means to describe massless objects and waves with momentum equivalent to their massive counterparts. Introduxing Planck's constant, quantised the relativistic energy and allowed working with manifest in the same terms of energy and momentum as massive entities.
______
c=\/h^2.f.L

That frequency and wavelength are related according only to c, c is directly dependant only on the value of another constant.

 

[bobc2]

I am extremely confident that I will understand with there is a speed limit, and when I do I will be able to explain it in a few sentences. And I will ask why someone else who understood couldn't have done that. I know because it keeps happening. There is an explanation for why there must be a limit and why it is what it is.

It depends on who you are explaining it to. If he doesn't understand your language and terms you are using, you first have to teach him that. If you will first learn a little analytic geometry (affine coordinates, how to graph functions, etc.) and the Pythagorean theorem, then you will understand it after looking at my post #5 along with a simple two-line derivation of the Minkowski metric.

 

[bobc2]

I hypothesize that it is not a random coincidence that the square root of (m/e) exactly equals the speed limit. I think there is some connection between matter and energy and the speed limit.

You are not even close.

 

[bobc2]

From another thread:




This is excellent. I think this is headed in the right direction. Conceptually, the important form of the equation e=mc^2 is c=squarroot(m/e). The real question is why is the speed limit of the universe equal to the square root of the mass of any object divided by it's energy. I get the feeling that it must be, by the very definitions of what mass and energy are. I don't see it yet though. I think this is very close. Something to do with the fact that energy is motion. I will think about it. If anyone can illustrate why that must be so, please do.

The square root of mass divided by energy. Hmm...

You are going down the wrong path. First figure out what you have to go off and study to understand bcrowell's first post (he has written a first class book on gerneral relativity, but it may be advanced from where you seem to be with your background). Google special relativity and also spacetime diagrams and see what you come up with.

 

[bcrowell]

First figure out what you have to go off and study to understand bcrowell's first post (he has written a first class book on gerneral relativity, but it may be advanced from where you seem to be with your background).

He/she might find this easier going: http://www.lightandmatter.com/html_books/6mr/ch01/ch01.html A similar treatment is Palash B. Pal, "Nothing but Relativity," http://arxiv.org/abs/physics/0302045v1

 

[harrylin]

This argument doesn't make sense. There is no (direct) logical connection between the speed of an electron wave and the speed of a photon wave.

That wasn't implied; instead it implies that an electron will be increasingly light-like at higher velocities, and cannot possibly move faster than light.

Once you fix a set of postulates, there is a right answer.

The OP asked "What is causing the restriction". I interpreted this as a physical question, not a question about human postulates that formulate the restriction!

CosmicVoyager, did I understand you correctly?

Harald

 

[CosmicVoyager]

That wasn't implied; instead it implies that an electron will be increasingly light-like at higher velocities, and cannot possibly move faster than light.

The OP asked "What is causing the restriction". I interpreted this as a physical question, not a question about human postulates that formulate the restriction!

CosmicVoyager, did I understand you correctly?

Harald

Yes, I mean what is holding the light back. It is like an invisible hand jumps up in front of things at c and stops them from going faster.

I suspect my paradigm might be completely wrong and I need to shift, in which case I need why it is wrong explained. It seems the same as if I were adding more and more to an object to increase it's mass, then suddenly the mass stopped increasing, and I think "What the heck is going on?"

 

[bcrowell]

The OP asked "What is causing the restriction". I interpreted this as a physical question, not a question about human postulates that formulate the restriction!

It's impossible to do logical reasoning without starting from some assumptions. Failing to spell out one's assumptions is simply sloppy reasoning.

 

[nitsuj]

Quote: bcrowell
"Failing to spell out one's assumptions is simply sloppy reasoning"

Or sloppy social skills, in comprehension.


CAUTION: LOTS OF HOT AIR FROM AN ARMCHAIR

I think it looks like cosmicvoyager is looking for an answer that works for him, a subjective one that works for his current understanding of his question.

Many of the posts here more then answer his question. Chicken / egg sums it up.

Here is my best attempt.

CosmicVoyager, consider the relationship between time and speed. It is as much a "speed limit" as a "time limit". Or an "activity limit". to your own point space is a medium, "C" is the bandwidth of that medium.

Why does the medium have a limit?

I fall back to thinking about the theory of the universe expanding.

I believe it is expanding at the speed of light. I also believe it is the medium itself that is expanding. Perhaps that theory comes before the "speed limit".

Said differently, maybe something can't travel faster then the meduim is being "built".

From there, let's turn the idea on its head.

At rest we are traveling at the limit (with space itself as it expands) and its movement that reduces this effect. So from an observer perspective as something travels, towards "C", the limit, it is actualy, relative to the medium, traveling towards zero, also were time / activity stops. So an object moving at "C" is moving as fast as the medium (space).

From the perspective of the medium "C" is not the maximum, its the minimum. And zero is the maximum.

To reiterate points already made let's assume my suggested answer is fact. Your question still stands, however shifts to "why does expansion of the medium itself have a "speed limit"?". Anwsers have to have a context, and your question didn't provide one. Without context it can always be asked, "yea, but why?".

 

[bcrowell]

CosmicVoyager, consider the relationship between time and speed. It is as much a "speed limit" as a "time limit". Or an "activity limit". to your own point space is a medium, "C" is the bandwidth of that medium.

You haven't defined "activity," "bandwidth," or "medium" in this context.

I fall back to thinking about the theory of the universe expanding.

I believe it is expanding at the speed of light.

This is incorrect.

I also believe it is the medium itself that is expanding.

What medium are you talking about?

Perhaps that theory comes before the "speed limit".

What you've said above isn't a theory.

Said differently, maybe something can't travel faster then the meduim is being "built".

This doesn't make sense, because the speed limit exists in special relativity and also in spacetimes in GR that are not expanding. It also doesn't make sense because the speed limit is a universal local property of all spacetimes, independent of any features that differentiate one spacetime from another.

 

[nitsuj]

All that I said was after my comment: CAUTION: LOTS OF HOT AIR FROM AN ARMCHAIR

2nd, the OP is playing imagination games, not condutcing physics experiements. The OP wasn't satisfied with replies that answered the question well, from a physics perspective.

Also the question itself suggests a limited physics background.

Therefore he must be asking from some other perspective, hence just some fun food for thought.

Tearing apart my laughable post, is equaly laughable. It wasn't posted to see if it holds up to peer review. seems I am as bad at physics as you are with...

 

[nitsuj]

This doesn't make sense, because the speed limit exists in special relativity and also in spacetimes in GR that are not expanding.

I googled it and the first page that came up explained how GR included something called the "cosmological constant". Which compensates for the expansion of the universe. Off topic but still interesting, the article mentioned how Einstien called it his "greatest blunder".

 

[Doc Al]

All that I said was after my comment: CAUTION: LOTS OF HOT AIR FROM AN ARMCHAIR

That's no excuse.

2nd, the OP is playing imagination games, not condutcing physics experiements. The OP wasn't satisfied with replies that answered the question well, from a physics perspective.

And yet, this is a physics forum.

 

[CosmicVoyager]

Quote: bcrowell
"Failing to spell out one's assumptions is simply sloppy reasoning"

Or sloppy social skills, in comprehension.


CAUTION: LOTS OF HOT AIR FROM AN ARMCHAIR

I think it looks like cosmicvoyager is looking for an answer that works for him, a subjective one that works for his current understanding of his question.

Many of the posts here more then answer his question. Chicken / egg sums it up.

Here is my best attempt.

CosmicVoyager, consider the relationship between time and speed. It is as much a "speed limit" as a "time limit". Or an "activity limit". to your own point space is a medium, "C" is the bandwidth of that medium.

Why does the medium have a limit?

I fall back to thinking about the theory of the universe expanding.

I believe it is expanding at the speed of light. I also believe it is the medium itself that is expanding. Perhaps that theory comes before the "speed limit".

Said differently, maybe something can't travel faster then the meduim is being "built".

From there, let's turn the idea on its head.

At rest we are traveling at the limit (with space itself as it expands) and its movement that reduces this effect. So from an observer perspective as something travels, towards "C", the limit, it is actualy, relative to the medium, traveling towards zero, also were time / activity stops. So an object moving at "C" is moving as fast as the medium (space).

From the perspective of the medium "C" is not the maximum, its the minimum. And zero is the maximum.

To reiterate points already made let's assume my suggested answer is fact. Your question still stands, however shifts to "why does expansion of the medium itself have a "speed limit"?". Anwsers have to have a context, and your question didn't provide one. Without context it can always be asked, "yea, but why?".

I like this sort of creative thinking :-) It might not be true, but having the idea expands one awareness and you can keep it in your bag of tricks for future explanations.

"Your question still stands, however shifts to "why does expansion of the medium itself have a "speed limit"?"."

It wouldn't for me. It does not have a limit. That speed is the result of whatever propelled the expansion. It could have been faster or slower.

 

[nitsuj]

Phew, thank you (i mean it sincerely) Cosmicvoyager for your reply. It demonstartes, to me, that my response was close to the right context for your question.

"It wouldn't for me. It does not have a limit. That speed is the result of whatever propelled the expansion. It could have been faster or slower." Cool, I think that means you picture it the way I was trying desperatly to describe it.

 

[DrGreg]

Yes, I mean what is holding the light back. It is like an invisible hand jumps up in front of things at c and stops them from going faster.

Maybe you are thinking, why can't you travel at 99% the speed of light, then go just 2% faster and find yourself at 101% the speed of light? Well, when you are traveling at 0.99c your notions of distance and time change. To the outside observer it looks like you have only 1% further to go, but from your own point of view you still have 100% to go -- the speed of light relative to you is still 299792458 m/s and you are no nearer to it than when you started. To look at this mathematically, velocities don't "add" as u+v but as

\frac{u+v}{1+uv/c^2}​

In the example above, your final velocity isn't 1.01c but

\frac{0.99c+0.02c}{1+0.99\times0.02}=0.99039c​

Another way of looking at this: the usual way to measure speed is to take distance on the observer's ruler divided by time on the observer's clock. But there is another way: take distance on the observer's ruler divided by time on the traveller's clock. This method is called "celerity" (or "proper velocity", a name I don't like). It turns out that the celerity of light is infinite, so if you translate your question from speed into celerity, "why is the universal celerity limit infinite?" it's a bit of a non-question.

You may well ask, "Why don't speeds add up" or "Why is the celerity of light infinite yet its speed is finite?" and most books will send you in a circle: "Because the speed of light is invariant" (the same for all observers), so it hasn't really answered your question. That's just the way the Universe is, who can say why?

 

[nitsuj]

Doc Al,

"That's no excuse." That's subjective.

"And yet, this is a physics forum." Actualy it's a physics forum.

 

[Ferrus]

http://golem.ph.utexas.edu/category/2006/08/letter_from_grothendieck.html

'One story has it that Grothendieck is now convinced that the Devil is working to falsify the speed of light. Schneps ascribes his concerns with the speed of light to his anxiety about the methodological compromises physicists make. He talks constantly, however, about the Devil, semi-metaphorically, sitting behind good people and nudging them in the direction of compromise, of the fudge, of the move towards corruption. ‘Uncompromising’ is the expression Schneps favours.'

 

[pip1974]

I think I understand what CosmicVoyager is getting at. It is fascinating and illuminating to start gaining an understanding of the implications of relativity from basic principles, i.e. the experimentally verifiable facts that light is observed to have the same speed for every observer and also that every frame of reference is equally valid. From that, we can explain and describe almost everything we can observe. But what's missing is the 'why' bit. And whether you like it or not, it's the 'why' bit that is the fundamental part of human nature that drives us to discover more and more about the universe.
CosmicVoyager is just wondering what it is about the fabric of the universe that makes things behave like this.
Nitsuj talked about some 'medium' expanding, but actually it is space that is expanding in every direction.
Isn't it the case that if time and space began with the big bang and has been getting bigger ever since, that the space I'm sitting in right now is an inflated bit of space that was once, and still is part of the big bang?
It isn't unreasonable to muse on the possibility that this stretching of space time in all directions has something to do with what we observe as a speed limit.

 

[Calrid]

Why is any constant what it is fine structure constant or c?

It's a superbly interesting question with no real coherent answer, only plenty of good ideas.

"There is only one thing faster than the speed of light and that is the speed of rumour."

Terry Pratchett, I'm paraphrasing.

Limits are troubling they make fools of us all I think.

 

[Dale]

But what's missing is the 'why' bit. And whether you like it or not, it's the 'why' bit that is the fundamental part of human nature that drives us to discover more and more about the universe.

hi pip1974, welcome to PF

Perhaps it is just the fact that I have young kids, but IMO "why" is generally not that important a question. any answer to a why question can be, and often is, simply followed by another why question. It is a game that any four-year old can play expertly. also, in my experience, generally a why question is asking for a bedtime story rather than a scientific experiment.

 

[Calrid]

hi pip1974, welcome to PF

Perhaps it is just the fact that I have young kids, but IMO "why" is generally not that important a question. any answer to a why question can be, and often is, simply followed by another why question. It is a game that any four-year old can play expertly. also, in my experience, generally a why question is asking for a bedtime story rather than a scientific experiment.

Why?

 

[Dale]

Once upon a time ...

 

[Calrid]

Once upon a time ...

Oooh! Does it have dragons!

 

[harrylin]

Why?

Yes exactly, why!
I agree with you. Children who never ask asking why (each time one level deeper) become scientists!

PS: the original popular reply to the "why" is because of the existence of a universal medium (Lorentz etc.), and the most popular reply today is because of the existence of a physical spacetime (Minskowski etc.). And likely there are numerous variants on those ideas and many other (such as post #16).

 

[pip1974]

hi pip1974, welcome to PF

Perhaps it is just the fact that I have young kids, but IMO "why" is generally not that important a question. any answer to a why question can be, and often is, simply followed by another why question. It is a game that any four-year old can play expertly. also, in my experience, generally a why question is asking for a bedtime story rather than a scientific experiment.

"Why?" is the most important question! And in science leads to the next level of understanding and more questions, that normally begin with "Why...".
Like, "Why do the planets appear to move the way they do?" Kepler already had equations to describe the motion of the planets and still Newton asked the question "why" because he felt that there were links to be made, patterns to be found and ideas to be brought together.
As I said before, it is human nature to ask the magic question "why" and to seek patterns in the things we experience and it is at the root of all scientific discovery. It is the same evolutionary trait that allowed our ancestors to be better hunter gatherers and to avoid predators that drives us to ask questions like "Why is there a universal speed limit".
Actually the simple answer to this particular question is that we don't know. Yes, we know that in the representation of the universe as we understand it that there is a speed limit, that there has to be one, and that it is based on the assumption that quite basic facts are true, but we do not know the real underlying nature of this speed limit or what the actual fabric of space itself is really like. We are still coming up with theories that try to model what the universe is really like deep down in the finest detail, but as we know the best theories are incompatible with each other.
And I think when kids want a story, and they ask "why this" or "why that" it's because we were all little scientists when we were kids. At some point, some people feel they have enough rules established to allow them to get by in their particular environment, whether they are a banker, a truck driver, an engineer or a physics teacher. But some people, bless them, just can't let things lie and keep on asking "why" and end up being scientists, philosophers, priests or artists.

 

[bobc2]

...It seems there is not reason there should be limits, and if there is, what is limiting factor? What is causing the restriction?

The reason there is a limiting factor for speeds is that the ever increasing speeds lead to a convergence of the X4 and X1 dimensions as they rotate toward each other (see sequence of sketches below). Then, the next "why question" is, "Why does the X1 coordinate rotate so as to maintain symmetry with X4 about the photon world line (note that this symmetry, with 45 degree photon world line, results in the same speed of light for all observers)?" A possible answer:

Nature wanted all observers to live with the same rules of physics, and this was the only way to do it (thus, nature contrived coordinates with invariance under Lorentz transformations)

 

[nitsuj]

pip1974 - "Nitsuj talked about some 'medium' expanding, but actually it is space that is expanding in every direction."

The "medium" I talked about is space/time.

To say it differently I was describing space/time as a medium.

It is not just space that is expanding, time is as well.