I Why does relativity not affect the speed of light?

[parshyaa]

Why speed of light is independent of frame of reference,why is it constant everywhere, speed of an object is different from different FOR then why this is not follwed by light, In deep space there is nothing to measure the speed of light relatively, then how it got its speed(299 792 458 m/s)
Please try to explain it in layman's term, because i haven't read special relativity or general relativity.

 

[fresh_42]

The invariance of the speed of light is the cause of relativity, not an effect.

Why it is everywhere the same? Because the universe has evolved this way.
How can we know? Because we measured it in various situations. I cannot list them, but a google search will probably do.

 

[DrClaude]

Physics doesn't answer such "why" questions. It appeared from experiments that all observers measure the same speed of light, whatever they speed or the speed of the light source. Using this as a given (a postulate), Einstein derived special relativity, and found that this leads to time dilation and length contraction. As @fresh_42 just wrote, these are consequences of the theory, the constant speed of light being the "cause."

 

[Dale]

It is possible to derive from some basic assumptions (homogeneity, isotropy, etc) that there are only two possibilities: either the invariant speed is finite (Einsteins relativity) or it is infinite (Galileos relativity). It is just a matter of experiment to determine which is correct.

 

[davidge]

It's worth remembering that invariance of the speed of light is observed in inertial frames, namely those in which the system acceleration vanishes. So if you don't have a intertial frame, there's nothing wrong with varying light speed.

 

[DrGreg]

speed of an object is different from different FOR then why this is not follwed by light

The relativistically correct formula for "adding" velocities (when you measure in a different frame) is$$
\frac{u+v}{1+ \frac{uv}{c^2}}
$$When $v$ is $\pm c$, the answer is still $\pm c$

 

[strangerep]

The invariance of the speed of light is the cause of relativity, not an effect.

Although that's the historical "2-postulate" approach, the modern "1-postulate" approach has it the other way around.
See @Dale's post #4.

 

[parshyaa]

It is possible to derive from some basic assumptions (homogeneity, isotropy, etc) that there are only two possibilities: either the invariant speed is finite (Einsteins relativity) or it is infinite (Galileos relativity). It is just a matter of experiment to determine which is correct.

Okk,We measure speed of anything with respect to something(ex: book on a table is at rest with respect to Earth but it is in motion with respect to moon), soo when light is in deep space(nothing to compare speed with) how can we measure its speed.
As you said speed of light is invariant, but above definition of speed is getting violated,we are not measuring it w.r.t something.

 

[Dale]

soo when light is in deep space(nothing to compare speed with) how can we measure its speed.

If you have a device to measure the speed of light then you can always use the device's frame if you wish, even in deep space.

If you do not have a device to measure the speed then you cannot measure the speed regardless of if it is in deep space or not.

 

[jbriggs444]

Okk,We measure speed of anything with respect to something(ex: book on a table is at rest with respect to Earth but it is in motion with respect to moon), soo when light is in deep space(nothing to compare speed with) how can we measure its speed.
As you said speed of light is invariant, but above definition of speed is getting violated,we are not measuring it w.r.t something.

A violation of theory would be an experiment producing a result that contradicts the theory. The lack of an experiment can never result in a violation.

 

[ImStein]

In deep space...

...is essentially a vacuum and a vacuum has properties! James Clerk Maxwell was able to calculate the speed of light from the properties of a vacuum in manifesting electric and magnetic fields. From this, he deduced (at Michael Faraday's prior suggestion) that light is an electromagnetic wave propagating at speed c. This matches the best measurements of light speed.

It is reasonable to surmise that if speed limit c (in a vacuum), is "universal" (i.e. the same everywhere in the universe) that it derives from the underlying structure of the universe. So far, from observations of distant objects, there is every reason to believe speed limit c is universal.

 

[Dale]

But again, all of that depends on your choice of units. The universality of c is tautological in SI units.

 

[Herman Trivilino]

Okk,We measure speed of anything with respect to something(ex: book on a table is at rest with respect to Earth but it is in motion with respect to moon), soo when light is in deep space(nothing to compare speed with) how can we measure its speed.

When we say the speed of light is the same for all observers what we mean is that if you measure it relative to something, you'll always get the same value.

 

[parshyaa]

When we say the speed of light is the same for all observers what we mean is that if you measure it relative to something, you'll always get the same value.

Yes and my question was how do we know that it is invariant(ie: its speed is constant relative to every FOR)

 

[russ_watters]

Yes and my question was how do we know that it is invariant(ie: its speed is constant relative to every FOR)

It's been measured a whole bunch of times in a whole bunch of different frames of reference (both directly and indirectly). Obviously it is inherently impossible to do any experiment everywhere, but "everywhere we have tried it" is a good enough reason to believe it is actually constant everywhere.

 

[parshyaa]

It's been measured a whole bunch of times in a whole bunch of different frames of reference. Obviously it is inherently impossible to do any experiment everywhere, but "everywhere we have tried it" is a good enough reason to believe it is actually constant everywhere.

You mean Just like law of conservation of mass is followed by many chemicals therefore we accept it as a law, there's no proof for that, we tested it with so many chemicals and we always got same results.

 

[russ_watters]

You mean Just like law of conservation of mass is followed by many chemicals therefore we accept it as a law, there's no proof for that, we tested it with so many chemicals and we always got same results.

I'm not sure how you are using the word "proof", but otherwise yeah, if we do a bunch of experiments and always get the same results, we conclude the theory is valid.

 

[russ_watters]

Also:

...soo when light is in deep space(nothing to compare speed with) how can we measure its speed.
As you said speed of light is invariant, but above definition of speed is getting violated,we are not measuring it w.r.t something.

I'm not sure what significance you place on "deep space" or why (all it means is we aren't there, which is kinda self-defeating), but I suspect there has been more testing of Relativity in space (deep or otherwise) than you realize. Perhaps the "deepest" is gravitational lensing, which has been observed over billions of light years (as well as within our own galaxy).
http://www.slate.com/blogs/bad_astronomy/2015/02/09/cosmic_smiley_a_happy_gravitational_lens.html

 

[Dale]

there's no proof for that, we tested it

You may want to read about Bayes' theorem and how it applies to making inductive inferences based on prior knowledge and new observations. It explains why we don't include unnecessary parameters in a model.

 

[Thecla]

Because of Galilean(or Newtonian ) Relativity, if you are in a train moving at constant velocity, there is no experiment that you can perform totally within the train that will tell you if the train is moving. With Maxwell and his equations in the middle of the nineteenth century(and the supposed existence of the ether) there was a means to measure the motion of the train. Einstein restored the old 17th century fact: You can not tell if the train is moving by an experiment inside the train. The constant measurement of the speed of light in all inertial frames is what saves the "you can't tell if the train is moving" phenomenon.

 

[Arkalius]

You mean Just like law of conservation of mass is followed by many chemicals therefore we accept it as a law, there's no proof for that, we tested it with so many chemicals and we always got same results.

Most scientific extrapolations are inductive in nature. That is to say, we derive a general rule from (many) specific examples. We can never conclusively "prove" scientific laws because there's no way we can exhaustively test every conceivable relevant scenario. When we use these inductions to generate explanations and precise predictions that end up coming true, this can offer further evidence that the induction is accurate, but in general we'll never know with 100% certainty that any scientific law applies as universally as the wording of it suggests.

 

[ImStein]

It is reasonable to surmise that if speed limit c (in a vacuum), is "universal" (i.e. the same everywhere in the universe) that it derives from the underlying structure of the universe. So far, from observations of distant objects, there is every reason to believe speed limit c is universal.

The universality of c is tautological in SI units.

Agreed. This is similar to the universality of π relating the structure of a circle. We now understand this is not merely the ratio of a circumference to a diameter but to the flatness of the surface in which it is embedded. A flat plane yields Euclidean geometry, with the standard value of π. But on a curved (non-Euclidean) surface, such as that of the earth, the ratio will be different, as the radius from a pole to the equator (a longitudinal arc) is different from the radius through the center of the earth. So, it's the underlying geometry that gives particular value to π. Indeed evaluating π is one way to test the flatness of space.

So, how might this apply to universal speed limit c? Consider Sean Carroll's depiction (guidebook p.77) of time. Like gravity or an electric field, it emanates from a charge, in this case the Big Bang event and one dimension up (a 4D temporal field). I've adapted his 2D cross section, by adding two spatial simultaneities as arcs "now" (t₁) and "future" (t₂). This is roughly consistent with the "balloon analogy" for cosmic expansion of space.

I've also drawn some worldlines indicating velocities. From a point "here, now" (red dot), zero velocity (V₀) is normal to space, while increasing velocities (V₁) find a natural and universal limit (V_max), tangent to space and enforced by the fundamental unidirectional nature of time. Thus, V_x is disallowed. In such a curved-space, radial-time model, space is derivative, providing bidirectional freedom to the extent that it does not violate the direction of time.

 

[PeterDonis]

In such a curved-space, radial-time model

Do you have a reference for this model, or is it just your personal construction? If it's the latter, please review the PF rules on personal theories.

 

[PeterDonis]

increasing velocities (V1) find a natural and universal limit (Vmax), tangent to space

This is incorrect as a description of any actual spacetime model--not just the one used in cosmology to describe our universe, but any model consistent with GR and the Einstein Field Equation. In any such model, a vector that is "tangent to space" will be spacelike, not null. (For example, your vector $V_x$ should be "tangent to space".) So your model does not appear to correctly represent the physics.

 

[PeterDonis]

In such a curved-space, radial-time model, space is derivative, providing bidirectional freedom to the extent that it does not violate the direction of time

This is true of any model consistent with GR and the Einstein Field Equation as well, so I don't see the point of your alternative, particularly as it contains a key error, pointed out in my last post.

 

[ImStein]

Do you have a reference for this [curved-space, radial-time] model, or is it just your personal construction?

The reference I gave clearly provides radial time, with respect to the Big Bang event (I believe it also appears in Sean Carroll's book on time.) There is no other way to represent a simultaneity there (where all locations measure the same age of the universe) than curved. Curved space is also given as the 3-surface in the familiar balloon analogy for the expanding cosmos.
"Just as space gets a direction [up] because we live in the vicinity of an influential object, the Earth, time gets a direction because we live in the vicinity of an influential event, the Big Bang." - Sean Carroll (caption to his radial, temporal field diagram)

In any such model, a vector that is "tangent to space" will be spacelike, not null. (For example, your vector Vx should be "tangent to space".) So your model does not appear to correctly represent the physics.

Yes, in Minkowski spacetime, "tangent to space" is the spatial coordinate of the given frame. That assumes flat space (locally, at least). Note that in the diagram as I adapted it, a lightlike interval remains null but it's direction is tangent to the given curved space (rather than having Minkowski's slope 1).

I don't see the point of your alternative...

I claim no privileged view of "reality" but PF has seen many threads asking essentially the same question (e.g. Why is there a finite universal speed limit?). Just glance at the "Similar Discussions" at the bottom of this page. This suggests that a tangible model would go a long way in satisfying them.

 

[PeterDonis]

The reference I gave

Is a pop science reference, not a textbook or peer-reviewed paper. I'm looking for the latter. Even if they are written by scientists who have published textbooks or peer-reviewed papers, pop science books and websites are not acceptable sources. If the scientist who wrote the book or website is really basing it on published, peer-reviewed science, he should provide a bibliography that tells you where that published, peer-reviewed science can be found.

 

[PeterDonis]

There is no other way to represent a simultaneity there (where all locations measure the same age of the universe) than curved

If by "there" you mean "in this specific diagram", then yes, of course, because you drew it that way. But if you are claiming that there is no way of drawing a spacetime diagram of our universe in which a spacelike hypersurface of constant comoving time (i.e., in which all comoving observers measure the same age of the universe) can be represented as flat, you are simply mistaken. In fact, in our current best-fit model of the universe, such hypersurfaces are flat, not just in a given representation (which might be distorted), but in reality--their spatial curvature is zero.

n Minkowski spacetime, "tangent to space" is the spatial coordinate of the given frame

That's true, but it's a much more specific statement than the one I was making. What I said was that in any spacetime, in any coordinate chart, any vector that is "tangent to space" will be spacelike, not null. That is an obvious consequence of the definition of "space" as a spacelike hypersurface, i.e., a hypersurface all of whose tangent vectors are spacelike. A hypersurface that does not have that property is not "space".

This suggests that a tangible model would go a long way in satisfying them.

Only if it properly represents the physics. Yours doesn't, as I've already pointed out.

 

[Dale]

This is similar to the universality of π relating the structure of a circle.

No, π is dimensionless, c is dimensionful. This analogy completely misses the whole point of the entire discussion.

 

[ImStein]

[Mysteries of the Universe: Time - by Sean Carroll] Is a pop science reference, not a textbook or peer-reviewed paper. I'm looking for the latter. Even if they are written by scientists who have published textbooks or peer-reviewed papers, pop science books and websites are not acceptable sources

I'll make a note of it. Carroll is a widely recognized and awarded educator. Though not peer reviewed, I don't think he's attempting to mislead anyone with his 24-lecture course on Time, which I've viewed four times and highly recommend.

in our current best-fit model of the universe, such hypersurfaces are flat, not just in a given representation (which might be distorted), but in reality--their spatial curvature is zero.

I understand your view but consider that current measures of flatness to provide only (an admittedly, very large) lower bound on any radius of curvature. Recall that science has repeatedly been surprised by prior estimates of the size of the universe. Also, when flat-looking representations of spacetime, such as Minkowski diagrams, admit to being non-Euclidean, aren't they effectively saying they aren't really flat?
"Minkowski space hence differs in important respects from four-dimensional Euclidean space."

the definition of "space" as a spacelike hypersurface, i.e., a hypersurface all of whose tangent vectors are spacelike.

Yes, but I believe the tangent vectors you refer to apply to curves occurring within the spatial 3-surface.
"Technically the three types of curves are usually defined in terms of whether the tangent vector at each point on the curve is time-like, light-like or space-like. ...One can also define the notion of a three-dimensional spacelike hypersurface, a continuous three-dimensional slice through the four-dimensional property with the property that every curve that is contained entirely within this hypersurface is a space-like curve."

The lightlike velocity vector (V_max) diagramed above is a tangent of the spatial 3-surface externally.

Only if it properly represents the physics. Yours doesn't,

As with flatness, you seem extraordinarily certain. Your model describes but does not explain a universal speed limit essential to physics. The model I gave does. Nevertheless, a "model" only approximates reality (and often only specific aspects of it), otherwise it would be reality.

No, π is dimensionless, c is dimensionful. This analogy completely misses the whole point of the entire discussion.

My impression is that both π and c are ratios of separations, thus ultimately dimensionless (without units). That is not to deny them meaning, specifically as the ratios apply to the underlying structure of their continuum. To the extent such ratios are universal, I believe they most simply reflect underlying structure of the universe, independent of anything else.

 

[PeterDonis]

when flat-looking representations of spacetime, such as Minkowski diagrams, admit to being non-Euclidean, aren't they effectively saying they aren't really flat?

No. "Flat" in the context of spacetime means "Minkowski". More generally, "flat" for any manifold with a well-defined Riemann tensor means the Riemann tensor vanishes. Minkowski spacetime satisfies that definition.

I believe the tangent vectors you refer to apply to curves occurring within the spatial 3-surface

Doesn't matter. Any curve that stays within a spacelike hypersurface will have tangent vectors that are everywhere spacelike.

The lightlike velocity vector (Vmax) diagramed above is a tangent of the spatial 3-surface externally.

No, it isn't. No lightlike vector can be tangent to any curve that lies entirely within a spacelike hypersurface. See above. The fact that your drawing represents it that way means your drawing is wrong.

As with flatness, you seem extraordinarily certain.

That's because I am. I'm talking about precise definitions (of flatness) and proven mathematical theorems (about the properties of tangent vectors that I stated above). If you're not familiar with the relevant math, I strongly suggest that you become so. A good, if advanced, reference is Hawking & Ellis.

Your model describes but does not explain a universal speed limit essential to physics.

For your definition of "explain", perhaps not. For my definition of "explain", saying that the "universal speed limit" is a geometric property of spacetime is just fine as an explanation.

The model I gave does.

No, it doesn't, because it's incorrect. See above. An incorrect model can't explain anything.

 

[Dale]

My impression is that both π and c are ratios of separations, thus ultimately dimensionless

No, this is clearly wrong. Obviously c is dimensionful, its value changes with different unit choices and in SI units it has dimensions of L/T. In contrast, the value of π does not depend on the units and it has no dimensions in any system of units.

If you wish to pursue this line of reasoning, please provide a professional scientific reference which agrees with your reasoning.

 

[PeterDonis]

Though not peer reviewed, I don't think he's attempting to mislead anyone with his 24-lecture course on Time,

I don't think he's attempting to mislead either, but the fact remains that in anything that is done for a lay audience, scientists can get away with things that they could not get away with in a peer-reviewed publication. For whatever reason, it seems that few if any scientists are capable of not doing so. My personal belief is that, without the pushback of peer review to call them on it when they go beyond what is established, scientists, being human, simply aren't capable of being careful enough about what they say.