Is the speed of light always 299 792 458 m / s

[Bjarne]

The speed of light is measured to 299 792 458 m / s and 1 meter defined to 1/299 792 458 of the speed of light.

Let us assume that A live at the top of a skyscraper and B in the cellar the past 10 billion years.

After 10 billion years B’s clock have “lost” (let's say) 10 second due to different gravitational influence, compared to A’s clock.

10 billion years ago 2 photons was leaving a star 10 billion light years away
and hit A and B at (almost) the same moment (splitsecond) 10 billion year after.

B would now say that he measured the time it took for the photon to reach earth to 10 second less than A measured.

B would therefore claim that either the speed of light must have been faster than 299 792 458 m / s, or local distance (where B is) must be different (stretching proportional with the stretch of time).

Which option is correct, and what proves it ?

Edited June 22, 2013 by Bjarne

[Markus Hanke]

10 billion years ago 2 photons was leaving a star 10 billion light years away

 

As measured by whose clock and whose ruler ?

[Bjarne]

As measured by whose clock and whose ruler ?

 

According to the example, we have in this case 2 observers

 

One observer "A" in the top of the skyscraper

The other "B" in the Cellar of the same skyscraper

 

Both have measure the time it took the photons to reach the earth.

B's clock shows that the 2 photon was 10 second faster to reach the Earth ( to reach the skyscraper) compared to A's clock.

 

So how can A and B agree about the speed of the photons.

 

Let's say A would claim that he is 110% sure that the photons was travelling with the speed 299792458 m/s (because this is what is written in the book).

 

This statement leaves B with only 2 options.

1.) Either B's ruler cannot be the same comparable length as A's ruler

2.) Or - (if the length of the ruler is a comparable universal standard) - the speed of light (299792458 m/s) is not the same for all observers.

 

Which option is correct?

Edited June 23, 2013 by Bjarne

[xyzt]

According to the example, we have in this case 2 observers

 

One observer "A" in the top of the skyscraper

The other "B" in the Cellar of the same skyscraper

 

Both have measure the time it took the photons to reach the earth.

B's clock shows that the 2 photon was 10 second faster to reach the Earth ( to reach the skyscraper) compared to A's clock.

 

So how can A and B agree about the speed of the photons.

 

Let's say A would claim that he is 110% sure that the photons was travelling with the speed 299792458 m/s (because this is what is written in the book).

 

This statement leaves B with only 2 options.

1.) Either B's ruler cannot be the same comparable length as A's ruler

2.) Or - (if the length of the ruler is a comparable universal standard) - the speed of light (299792458 m/s) is not the same for all observers.

 

Which option is correct?

A distant observer disagrees about the "coordinate" speed of light: [math]c_r=c(1-r_s/r)[/math] at points A and B.

[math]r_s[/math] is the Schwarzschild radius of the Earth

[math]c[/math] is the local speed of light (a universal constant)

[math]r[/math] is the radial coordinate

 

So, a distant observer measures: [math]c_A/c_B=(1-r_s/r_A)/(1-r_s/r_B)[/math]

 

The "disagreement) is not 2 seconds, it is much less than that but this is irrelevant since:

 

A and B agree on the "local" speed of light.

Coordinate dependent entities are not meaningful in GR (and in physics, in general).

Edited June 23, 2013 by xyzt

[Bjarne]

A and B disagree about the "coordinate" speed of light: [math]c_r=c(1-r_s/r)[/math].

[math]r_s[/math] is the Schwarzschild radius of the Earth

[math]c[/math] is the local speed of light (a universal constant)

[math]r[/math] is the radial coordinate

 

So: [math]c_A/c_B=(1-r_s/r_A)/(1-r_s/r_B)[/math]

 

The "disagreement) is not 2 seconds, it is much less than that but this is irrelevant since:

 

A and B agree on the "local" speed of light.

Coordinate dependent entities are not meaningful in GR (and in physics, in general).

 

Try to explain further how you define "local" speed.

Which comparable difference would it be between A's and B's definition of local speed of light ?

 

So fare I understand, A and B have only 3 mathematical factors to deal with here, - one is speed, - the other is time, - the (third), the result = distance.

 

Time multiplied with speed must be = distance.

 

If A and B both agree that the speed of light is a universal constant that always is local "the same", - for any observer, we do have a problem, - unless A and B's ruler not is comparable the same length .

 

It is a fact that A and B does not agree about the time it took for 2 photons to travel to the Earth.

If we say that A has counted the photons travel-time to 10 second more than B, - A must also have calculated the distance to the star emitting the photon (time*speed) to (10 * 300.000 km) = 3.000.000 km more than B.

 

So how can the distance not be the same for A and B ?

Must the distance be the same ?

 

The only logical option I can see , - is that the ruler is simply not comparable the same length (seen from A and and B's perspective / in the cellar and top of the skyscraper).

Which mean, - because 1 second on B's clock (compared to A's clock) is "stretching" (due to gravity difference) - B's ruler must compared to A's ruler (proportionally) do the same.

And therefore B' will simple measure / calculate a different (shorter) distance than A to the star, - that 10 billion years ago was emitting the photons now hitting A and B in the same moment.

 

I mean, - there must be a logical and simple explanation to that A and B not is able to agree about the distance to that star.

 

Or ?

 

 

You do not really understand something unless you can explain it to your grandmother.

Albert Einstein

Edited June 23, 2013 by Bjarne

[xyzt]

I mean, - there must be a logical and simple explanation to that A and B not is able to agree about the distance to that star.

What gives you the idea that "A and B are not able t agree about the distance to that star"?

Try to explain further how you define "local" speed

The local speed of light is central to GR, it appears in the solution of the Einstein Field Equations (EFE). For example, it appears in the Schwarzschild solution:

 

[math]ds^2=(1-r_s/r) c^2dt^2-dr^2/(1-r_s/r)[/math]

 

Light follows null geodesics, so:

 

[math]0=(1-r_s/r) c^2dt^2-dr^2/(1-r_s/r)[/math]

 

From the above, you can get the {coordinate" (as opposed to "local") speed of light:

 

[math]c_r=\frac{dr}{dt}=c(1-r_s/r)[/math]

 

as I explained to you in a previous post.

 

Looks like you want to "challenge" SR/GR. My advice to you is to start by studying.

Edited June 23, 2013 by xyzt

[Bjarne]

What gives you the idea that "A and B are not able t agree about the distance to that star"?

The local speed of light is central to GR, it appears in the solution of the Einstein Field Equations (EFE). For example, it appears in the Schwarzschild solution:

 

[math]ds^2=(1-r_s/r) c^2dt^2-dr^2/(1-r_s/r)[/math]

 

Light follows null geodesics, so:

 

[math]0=(1-r_s/r) c^2dt^2-dr^2/(1-r_s/r)[/math]

 

From the above, you can get the {coordinate" (as opposed to "local") speed of light:

 

[math]c_r=\frac{dr}{dt}=c(1-r_s/r)[/math]

 

as I explained to you in a previous post.

 

Looks like you want to "challenge" SR/GR. My advice to you is to start by studying.

Sorry, - but I am afraid that if I would tell all that to my grandmother, - se would not understand anything, (and accuse me for the same)

 

All I want is only have logical simple answers, - to a logic simple question.

 

I mean time multiplied with speed must = distance.

This is so simple as something can be.

 

A and B doesn't agree about time, - it takes a photon to travel the mentioned distance (10 billion LY) - if they agree about speed of the photon, - the result must be different distant.

 

How can A and B then agree about the distance the photons travels ?

 

The math you have shown is above my head, I only need a simple questions as possible.

 

You wrote "Light follows null geodesics, so" - The photon I mention in the thought experiment, followed the same path, both seen from A's and B's perspective.

 

I am not trying to challenge GR, but rather trying to understand it, down to earth.

 

We can instead use a thought experiment where you have a car driving round the earth lets say at the speed 100 m/s none stop 10 billion years

 

If A and B must agree about the speed....100 m/s .

A's clock would now also show that the car-race took longer time than counted at B's clock.

 

Now A will calculate the distance the car have travel (10 billion years) and then claim that the car must have reach a longer distance, - than the distance B have calculated.

 

Simple because A's clocks ticks faster in the top of the skyscraper than B's clock in the cellar. - All based on the simple fact, - that time multiplied with speed = distance.

 

So what is "wrong" ?

 

The answer must be simple, down to earth (regardless how complicated GR math can be).

[xyzt]

A and B doesn't agree about time, -

What gives you this idea? (Hint: it is wrong).

[doG]

The speed of light is measured to 299 792 458 m / s and 1 meter defined to 1/299 792 458 of the speed of light.

 

 

 

That is the reference speed of light in a vacuum, not the speed of light under other circumstances.

[md65536]

Which option is correct, and what proves it ?

I'll modify your original example to make it easier to talk about.

 

Imagine that observer A and the star are stationary in flat spacetime, so their clocks tick at the same rate. They're 10 billion LY apart. A burst of light from the star takes 10 billion years to cross the distance according to A's clock.

 

Imagine that you place 10 billion rulers, each 1 LY long, end to end between A and the star. This measures the proper distance or ruler distance between the two, and all observers will agree that there are 10 billion of them between the two. You could also put a clock at each ruler, and each clock would measure that light crosses its ruler in one year.

 

Now consider observer B in a lower gravitational potential so that B's clock is ticking at half the rate of A's. While A's clock has ticked 10 billion years, B's has only ticked 5 billion. Also, while each of the rulers' clocks ticks 1 year, B's clock only ticks half a year. Yet... B agrees that there are 10 billion rulers between the star and A, since proper distance is invariant. If you say that B observes the photons crossing a 1 LY ruler in 0.5 years, then you're comparing the distance measured by one of the distant rulers to a time measured at B, and that doesn't really matter so much, because "the local speed of light is c" means that it crosses a 1 LY ruler in 1 year according to a clock at the ruler (not that 1 LY is usually "local" but it works in this case).

 

(There are also different measures of distance that you could use, with which A and B might not measure the same distance between A and the star.)

 

So, B could say that it took less time by its own clock, for the light burst to travel from the star to A, but it wouldn't use that to define the speed of light.

Edited June 24, 2013 by md65536

[xyzt]

 

 

Now consider observer B in a lower gravitational potential so that B's clock is ticking at half the rate of A's.

In order for the above to happen you need to have :

 

[math]\sqrt{\frac{1-r_s/r_a}{1-r_s/r_B}}=2[/math]

 

i.e.

 

[math]r_B=\frac{4r_s}{3+r_s/r_A} \approx \frac{4r_s}{3}[/math]

 

This is non-physical given that [math]r_s[/math] is the Schwarzschild radius. Even if it were possible, the disparity between [math]r_A[/math] and [math]r_B[/math] explains why the two observers have very differing distances to the star in question.

 

The more normal case, as in the case of the Pound-Rebka experiment, the two observers (A and B) are separated by a few meters and theirs clocks are ticking at rates very close to each other. I am quite sure that the difference in clock rates is cancelled out by the differences in distances to the Schwarzschild observer (situated on the distant star).

Edited June 24, 2013 by xyzt

[md65536]

The more normal case, as in the case of the Pound-Rebka experiment, the two observers (A and B) are separated by a few meters and theirs clocks are ticking at rates very close to each other. I am quite sure that the difference in clock rates is cancelled out by the differences in distances to the Schwarzschild observer (situated on the distant star).

I used a value of 2 to more easily imagine the clocks with extreme time dilation instead of a few seconds over 10 billion years. It's not very physically practical but it could be done by having B near a black hole and A far away in empty space. The distance between A and B doesn't directly affect the measurements of timing or distance of between A and the star.

 

A's and B's clocks tick at a different rate. What do you mean by that the difference would cancel out? You don't need to care about the distance from B to the star to be able to say that B calculates a shorter duration on its clock, for a signal to travel from the star to A, than A does by its own clock. A's clock is ticking faster.

Edited June 24, 2013 by md65536

[Bjarne]

I'll modify your original example to make it easier to talk about.

 

Imagine that observer A and the star are stationary in flat spacetime, so their clocks tick at the same rate. They're 10 billion LY apart. A burst of light from the star takes 10 billion years to cross the distance according to A's clock.

 

Imagine that you place 10 billion rulers, each 1 LY long, end to end between A and the star. This measures the proper distance or ruler distance between the two, and all observers will agree that there are 10 billion of them between the two. You could also put a clock at each ruler, and each clock would measure that light crosses its ruler in one year.

 

Now consider observer B in a lower gravitational potential so that B's clock is ticking at half the rate of A's. While A's clock has ticked 10 billion years, B's has only ticked 5 billion. Also, while each of the rulers' clocks ticks 1 year, B's clock only ticks half a year. Yet... B agrees that there are 10 billion rulers between the star and A, since proper distance is invariant. If you say that B observes the photons crossing a 1 LY ruler in 0.5 years, then you're comparing the distance measured by one of the distant rulers to a time measured at B, and that doesn't really matter so much, because "the local speed of light is c" means that it crosses a 1 LY ruler in 1 year according to a clock at the ruler (not that 1 LY is usually "local" but it works in this case).

 

(There are also different measures of distance that you could use, with which A and B might not measure the same distance between A and the star.)

 

So, B could say that it took less time by its own clock, for the light burst to travel from the star to A, but it wouldn't use that to define the speed of light.

I fully agree

 

I used a value of 2 to more easily imagine the clocks with extreme time dilation instead of a few seconds over 10 billion years. It's not very physically practical but it could be done by having B near a black hole and A far away in empty space. The distance between A and B doesn't directly affect the measurements of timing or distance of between A and the star.

 

A's and B's clocks tick at a different rate. What do you mean by that the difference would cancel out? You don't need to care about the distance from B to the star to be able to say that B calculates a shorter duration on its clock, for a signal to travel from the star to A, than A does by its own clock. A's clock is ticking faster.

 

Lets say a trip between Barcelona and New York takes 10.000 seconds.

Let's say that tomorrow morning when we wake up, we are on board a space craft and very close to a black hole.

The clock is now ticking 10.000 time slower than on Earth, and the trip from Barcelona to New York, - seen from our perspective, - would now only take 1 second.

 

What would happen if it was possible to compare our ruler (on board) with a ruler back on Earth ? - would they be comparable the same length ?

How sure can we be ?

 

Seen from the perspective of a photon, time doesn't exist, and therefore distance cannot exist.

So seen from the photons own perspective, - it must be everywhere at the same time.

I know this doesn't sound logical but this is a mathematical consequence.

So it is not unknown that relativity must change distances as well.

 

In the same way, - I believe, - if our space craft should reach the event horizon, - time is no longer ticking, - which also must mean that distance no longer exist (?)

The trip between Barcelona and New York will now (from our perspective) take zero seconds.

 

So at the event horizon I think it is fair to conclude that distant no longer exist, we must have reached the reality of the photon, - where everything must happen "at the same moment"

But the lose of distance cannot happen suddenly, its not logical, - it must most likely happen gradually and proportional with the lose of time, I believe.

Edited June 24, 2013 by Bjarne

[John Cuthber]

"Is the speed of light always 299 792 458 m / s?"

Yes.*

http://physics.nist.gov/cuu/Units/current.html

 

* strictly, it's the speed of light in vacuo.

[xyzt]

You don't need to care about the distance from B to the star to be able to say that B calculates a shorter duration on its clock, for a signal to travel from the star to A, than A does by its own clock. A's clock is ticking faster.

A and B are not at the same distance from the star, I thought that I made that quite clear. A is closer to the star and A clock ticks faster. B is farther from the star and B clock ticks slower.

A radar signal sent from A to the star makes the roundtrip in [math]\Delta t_A=\frac{2d_A}{c}[/math] (google "Shapiro delay"). [math]d_A[/math] is the distance between A and the star.

A radar signal sent from B to the star makes the roundtrip in [math]\Delta t_B=\frac{2d_B}{c}[/math].

 

In both cases, contrary to what Bjarne is trying to claim, the speed of the radar signal is the same , "c".

Edited June 24, 2013 by xyzt

[Delta1212]

A and B are not at the same distance from the star, I thought that I made that quite clear. A is closer to the star and A clock ticks faster. B is farther from the star and B clock ticks slower.

A radar signal sent from A to the star makes the roundtrip in [math]\Delta t_A=\frac{2d_A}{c}[/math] (google "Shapiro delay"). [math]d_A[/math] is the distance between A and the star.

A radar signal sent from B to the star makes the roundtrip in [math]\Delta t_B=\frac{2d_B}{c}[/math].

 

In both cases, contrary to what Bjarne is trying to claim, the speed of the radar signal is the same , "c".

It's possible I'm missing something and the star isn't the source of gravity in this discussion, but wouldn't the clock closest to the star tick slower than the one farther away? Edited June 24, 2013 by Delta1212

[xyzt]

It's possible I'm missing something and the star isn't the source of gravity in this discussion, but wouldn't the clock closest to the star tick slower than the one farther away?

The star is very far away, A and B are near a DIFFERENT gravitating body.

[swansont]

A and B are not at the same distance from the star, I thought that I made that quite clear. A is closer to the star and A clock ticks faster. B is farther from the star and B clock ticks slower.

A radar signal sent from A to the star makes the roundtrip in [math]\Delta t_A=\frac{2d_A}{c}[/math] (google "Shapiro delay"). [math]d_A[/math] is the distance between A and the star.

A radar signal sent from B to the star makes the roundtrip in [math]\Delta t_B=\frac{2d_B}{c}[/math].

 

In both cases, contrary to what Bjarne is trying to claim, the speed of the radar signal is the same , "c".

 

!

Moderator Note

Bjarne made no mention of a round-trip radar signal. Please stick to the original formulation of the problem, and not muddy the discussion.

[xyzt]

!

Moderator Note

Bjarne made no mention of a round-trip radar signal. Please stick to the original formulation of the problem, and not muddy the discussion.

One way light speed is not measurable, this is a well known fact in mainstream physics world. Only two-way light speed can be measured, the Shapiro delay type of experiments do this routinely at the cosmological levels (see any GR textbook).

[md65536]

A and B are not at the same distance from the star, I thought that I made that quite clear. A is closer to the star and A clock ticks faster. B is farther from the star and B clock ticks slower.

A radar signal sent from A to the star makes the roundtrip in [math]\Delta t_A=\frac{2d_A}{c}[/math] (google "Shapiro delay"). [math]d_A[/math] is the distance between A and the star.

A radar signal sent from B to the star makes the roundtrip in [math]\Delta t_B=\frac{2d_B}{c}[/math].

 

In both cases, contrary to what Bjarne is trying to claim, the speed of the radar signal is the same , "c".

I agree with all those statements, except now you're using radar distance instead of proper distance.

 

Using the original values, the radar distance from A to the star is 10 billion light years, and the radar distance from B to the star is 10 billion light years + 10 light seconds. A and B are not separated by 10 light seconds. Their measurements of radar distance differ.

 

!

Moderator Note

Bjarne made no mention of a round-trip radar signal. Please stick to the original formulation of the problem, and not muddy the discussion.

I agree with xyzt and think that including radar signals helps clarify the answers. Without it, the timing differences could be confused with a problem of simultaneity. I'll try to stay on topic.

[Delta1212]

 

The star is very far away, A and B are near a DIFFERENT gravitating body.

Ok, that makes sense.

[md65536]

Lets say a trip between Barcelona and New York takes 10.000 seconds.

Let's say that tomorrow morning when we wake up, we are on board a space craft and very close to a black hole.

The clock is now ticking 10.000 time slower than on Earth, and the trip from Barcelona to New York, - seen from our perspective, - would now only take 1 second.

One second by our clock, but still 10 seconds according to a traveler's clock. There's not a lot of point of saying the trip takes one second, because we can't make that trip while maintaining a clock that ticks at a tenth the rate. If you brought a ruler stretching from Barcelona to NY into our extreme gravitational field, it would take 10 seconds by our clock to cross it.

What would happen if it was possible to compare our ruler (on board) with a ruler back on Earth ? - would they be comparable the same length ?

How sure can we be ?

Well... it depends on how you compare them, ie. what definition of distance is used. The proper length of a 1m ruler is 1m according to any observer -- it is invariant. You can be sure because a clock at the ruler, anywhere, will measure light to take 1m/c to cross the ruler.

There are other measures of distance.....

So seen from the photons own perspective, - it must be everywhere at the same time.

I know this doesn't sound logical but this is a mathematical consequence.

[...]

The trip between Barcelona and New York will now (from our perspective) take zero seconds.

[...]

But the lose of distance cannot happen suddenly, its not logical, - it must most likely happen gradually and proportional with the lose of time, I believe.

No, it's not a mathematical consequence. It's not logical, yet math is logical. A photon doesn't have a perspective, but even if you say the universe contracts to 0 length, the photon still has 0 size and isn't "everywhere". The photon doesn't have a clock; there's no measure of time for which you can pick a moment from the photon's perspective. Meanwhile, the photon is only ever between Barcelona and NY in this example, and picking a moment using any clock will put the photon at only a single location (classically). Even if our clock slows to a stop, and distant clocks seem to tick at an infinite rate, we don't lose all sense of time, and we still know that a trip between Barcelona and NY still takes 10 seconds according to those distant clocks.

 

I'm not sure if the appearance of this stuff would be gradual or not. If you fell into a black hole and your distant sun's clock ticked at an extreme rate, could you receive its lifetime of light output in a brief flash? I don't know how to make sense of that.

[xyzt]

I agree with all those statements, except now you're using radar distance instead of proper distance

This is standard in cosmology: proper distance isn't available (for practical reasons). The only available (measurable) distance is radar distance.

[Bjarne]

One second by our clock, but still 10 seconds according to a traveler's clock.

 

Sorry I put a dot not a comma, I mean time near the black hole was 10,000 slower not only 10 times.

 

 

 

There's not a lot of point of saying the trip takes one second, because we can't make that trip while maintaining a clock that ticks at a tenth the rate.

 

The trip from Barcelona to NY took 1 second seen from a extreme space-time perspective ( a spacecraft near a black hole). On earth it still take 10,000 seconds

 

 

If you brought a ruler stretching from Barcelona to NY into our extreme gravitational field, it would take 10 seconds by our clock to cross it.

 

I didn't got the point.

 

Well... it depends on how you compare them, ie. what definition of distance is used.

The proper length of a 1m ruler is 1m according to any observer -- it is invariant. You can be sure because a clock at the ruler, anywhere, will measure light to take 1m/c to cross the ruler.

There are other measures of distance.....

I think you misunderstood that, the point is that there is no way to compare 2 rules, in different space-time. Therefore we only have logical thinking left, when it comes to the question whether these are comparable the same length.

 

No, it's not a mathematical consequence. It's not logical, yet math is logical. A

The point is, to make it simple / mathematical logical.

 

photon doesn't have a perspective, but even if you say the universe contracts to 0 length, the photon still has 0 size and isn't "everywhere". The photon doesn't have a clock; there's no measure of time for which you can pick a moment from the photon's perspective.

Try to Google this "photons are everywhere at the same time"

 

Meanwhile, the photon is only ever between Barcelona and NY in this example, and picking a moment using any clock will put the photon at only a single location (classically).

You misunderstood that point, - photons was only mentioned in the last thought experiment (Barcelona-NY) to show that if times stops, distance doesn't exist. The same should (to my opinion) apply by the event horizon.

 

Even if our clock slows to a stop, and distant clocks seem to tick at an infinite rate, we don't lose all sense of time, and we still know that a trip between Barcelona and NY still takes 10 seconds according to those distant clocks.

The point here is , if you was by the event horizon, how would the universe then look like, - would there ne any universe at all ? - I believe it wouldn't, - if this is true rulers can most likely not be comparable the same length , different places in a gravitational field. Black holes, would then be geometric collapse etc...

 

I'm not sure if the appearance of this stuff would be gradual or not.

And this is the whole point.

 

 

If you fell into a black hole and your distant sun's clock ticked at an extreme rate, could you receive its lifetime of light output in a brief flash? I don't know how to make sense of that.

Good point

Photons and other particle moving at c, are in a reality where everything happens at the same moment.

But from that perspective "the moment" (time) doesn't exist, and also not distance, which mean the Universe doesn't exist.

I know this is completely crazy, and maybe therefore Niels Bohr he once wrote..."Your theory is crazy, but it's not crazy enough to be true"

At this extreme, don't even try to think any logical / rational thought,- just accept it is beyond our capacity .

 

I am only trying to understand whether 1 meter is a variant not only in SR, - but also in GR.

I think this question make sense, and must be possible to define based on simple math / logic .

[xyzt]

I am only trying to understand whether 1 meter is a variant not only in SR, - but also in GR

The simple answer is : coordinate length/time are variable in SR and in GR. Proper length/time is invariant in both SR and GR.