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

[md65536]

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 .

I'm trying to answer only in terms of GR, often trying to figure it out as I go. GR is not "beyond our capacity".

 

Yes, with a variant measure of distance, a length in GR can vary depending on observer.

 

 

BTW I figure you would not observe a distant star's lifetime in a brief flash, while near a black hole. If you imagine a line of rulers between you and the star, and suppose that the star's clock ticks at a rate approaching infinity, then you'd receive all that light in an instant only if all of the clocks along the line of rulers were also ticking at a rate approaching infinity, and that wouldn't be the case here. For example with a relatively "nearby" clock that ticks at only twice your rate, the light from the star would still take 1m/c to cross its meter stick during which your clock would need to tick (half as much).

[swansont]

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).

 

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.

 

!

Moderator Note

The point is this is Bjarne's thread, so discussion should be in context of the questions that Bjarne is asking, and not in terms of a new discussion that excludes the OP.

[Bjarne]

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

Shall we understand this, so that length contraction or expansion, are proportion with the stretch / contraction of time (1 second) ?

For example

You live in a deep cellar, time here ticks 1/100,000,000 times slower than on my clock, - does that mean that your ruler is also 1/100,000,000 times longer than my ?

 

I'm trying to answer only in terms of GR, often trying to figure it out as I go. GR is not "beyond our capacity".

 

Yes, with a variant measure of distance, a length in GR can vary depending on observer.

 

BTW I figure you would not observe a distant star's lifetime in a brief flash, while near a black hole.

If you imagine a line of rulers between you and the star, and suppose that the star's clock ticks at a rate approaching infinity, then you'd receive all that light in an instant only if all of the clocks along the line of rulers were also ticking at a rate approaching infinity, and that wouldn't be the case here. For example with a relatively "nearby" clock that ticks at only twice your rate, the light from the star would still take 1m/c to cross its meter stick during which your clock would need to tick (half as much).

I understand your point, - this is rational thinking

But GR can also cause time to stop..

This is so strange that I still believe this is beyond our understanding capacity, because our brains can only truly understand something when it happens in time / distance.

 

For example lets think about how does the universe look like if you was very close the event horizon.

A photon from the edge of the visible universe (13,8 LY away from Earth) can reach the earth (seen from a down to earth perspective) within 13,8 billion years.

But you would measure that the same event only took 10 second, because you and your clock is close to a black hole.

 

Now image it is real, you really live in the reality near the horizon event ...

 

How long time would it take you to drink a cup of coffee ?

How would it feel to do so ?

How big would you body be ? etc...

Would it all be same proportions "exactly" like on Earth?

Or would it be real slow motion to lift the cup to your month etc .....

Would you feel the 10 second it takes a photon from the distinct star to reach earth, - seen from your event horizon perspective, - in the same way as a person at the Earth feel the time it took based on Earth time (13,8 billion years)?

 

It can be hard to understand real slow motion "live" - as just mentioned (?)

But to understand that time no longer exist, I guess is completely impossible .

 

I am just wondering which (comparable) differences would we notice if we could jump between different space-time "realities"..

Maybe it help to understand the most extreme example first. (?) maybe not (?)

[xyzt]

Shall we understand this, so that length contraction or expansion, are proportion with the stretch / contraction of time (1 second) ?

For example

You live in a deep cellar, time here ticks 1/100,000,000 times slower than on my clock, - does that mean that your ruler is also 1/100,000,000 times longer than my

No, the correct formulas have been shown earlier here.

Edited June 25, 2013 by xyzt

[esbo]

Just to throw in my answer, B's world has contracted to due to the extra gravity, thus distance has changed and makes up for the change in time thus giving the same answer for C.

 

I just know I am right on this one so please tell me I am right and email me my Nobel prize for physics. (just the money I have no more room for trophies).

 

I mean B's rular has contracted (or expanded).

 

Any how point is the light arrives at the same time for both, so I am thinking this is to do with simultaneousness,

I mean lets face it they do not know what time the light was sent out only when it arrived.

 

So yea it does arrive at different times on each's clock (but at the same time really )

 

But the BIG thing is neither know when the light pulse was sent out, all they see is darkness until there is light.

 

I think that is the key point, the length contraction is a different minor issue I would imagine.

 

I guess you could learn more if he sent out two light pulse say 1000 seconds apart, that might be

a more meaningful problem, then again it might not especially if you made a mistake with your logic.

Edited June 26, 2013 by esbo

[Bjarne]

No, the correct formulas have been shown earlier here.

Wonder which kind of impact that would had on md65536's cup of coffee.

As I said, this math is above my head.

[md65536]

But GR can also cause time to stop..

This is so strange that I still believe this is beyond our understanding capacity, because our brains can only truly understand something when it happens in time / distance.

Fair enough, but I think it's important to differentiate between where GR doesn't make meaningful predictions (like at singularities?, or where time can "stop"), and where it might make predictions that can't practically be verified (such as inside a black hole, from which we could receive no useful information), and where it makes bizarre yet falsifiable predictions that are simply more extreme versions of what's already been verified. I don't think it's good to mix what can't meaningfully be predicted and what can, and say that both are beyond our capacity.

 

Anyway this is beyond *my* current capacity. I've been googling some questions and came across this: "Falling Into and Hovering Near A Black Hole" http://mathpages.com/rr/s7-03/7-03.htm

 

As an example here, the equations used in this thread break down at the Schwarzschild radius. Indeed it seems that as you approach that radius, all clocks everywhere in the universe may approach an infinite tick rate, and you would be fried by an eternity's worth of blue-shifted radiation from stars.* BUT this is the prediction for if you're hovering at that radius, and to do so would be equivalent to traveling at the speed of light or whatever... it would require infinite energy. It's not physically possible so it's not meaningful to predict what would happen if you did it.

 

* Edit: Dammit I change my mind again, for the third time at least. Here's an interesting excerpt from the link above:

relative to the frame of a particle falling in from infinity, a hovering observer must be moving outward at near light velocity. Consequently his axial distances are tremendously contracted, to the extent that, if the value of Dr is normalized to his frame of reference, he is actually a great distance (perhaps even light-years) from the r = 2m boundary, even though he is just 1 inch above r = 2m in terms of the Schwarzschild coordinate r. Also, the closer he tries to hover, the more radial boost he needs to hold that value of r, and the more contracted his radial distances become. Thus he is living in a thinner and thinner shell of Dr, but from his own perspective there's a world of room. Assuming he brought enough rocket fuel to accelerate himself up to this "hovering frame" at that radius 2m + Dr (or actually to slow himself down to a hovering frame), he would thereafter just need to resist the local acceleration of gravity to maintain that frame of reference.

The distances used in the equations in this thread are in Schwarzschild coordinates. Apparently that's not the same as the measurements in the hovering observer's local frame. And I think neither are the same as proper length. So there's many different possible measures of length, I think radar distance would be different too. Since the inch in Schrwarzschild coordinates is measured as "light years" in this excerpt, it would take years for light to cross such a distance to reach the observer in her own frame of reference, so again I think that no matter how close the observer gets to the horizon, she wouldn't be fried in an instant, because all of that radiation would still take years to arrive. Definitely confusing, I don't think I've solved it yet!

How long time would it take you to drink a cup of coffee ?

How would it feel to do so ?

How big would you body be ? etc...

Would it all be same proportions "exactly" like on Earth?

Or would it be real slow motion to lift the cup to your month etc .....

Would you feel the 10 second it takes a photon from the distinct star to reach earth, - seen from your event horizon perspective, - in the same way as a person at the Earth feel the time it took based on Earth time (13,8 billion years)?

I can't do the calculations. There are various things you could look up here: spaghettification etc. Falling into and hovering near an event horizon are different things. The bigger the Schwarzschild radius, the less the tidal forces... you would be stretched head to toe and squeezed sideways, but according to googled videos, you could survive falling through an event horizon of a big enough black hole (freefall, apparently you wouldn't even be able to detect the location of the horizon).

 

So, there are a lot of different parameters and possibilities, most of which I don't know. But supposing that you're not affected by such extreme tidal forces... in a small enough "local" area everything seems normal. So supposing that a clock say at your hands ticks at roughly the same rate as the one near your eyes, then you would experience drinking the coffee at a normal rate. A local clock ticks at one second per second. It is only slow relative to *other* clocks, not itself. So you wouldn't experience the "slowing of time", the slowing of your clock that others could measure.

 

Earth would appear brighter, blue-shifted, and aging at a fast rate.

Edited June 26, 2013 by md65536

[elfmotat]

bjarne, you appear to be under the impression that if two observers disagree about length or time then there is no meaningful way to compare measurements. That's simply not true. A meter is a meter is a meter.

 

In general the speed of light will not be the same for two observers in circular motion or near a gravitating body, because their clocks and rulers will differ. Locally (which means "over a small enough scale for a short enough time") the speed of light is always c.

[Markus Hanke]

As an example here, the equations used in this thread break down at the Schwarzschild radius.

 

What we find at the Schwarzschild radius is a coordinate singularity in Schwarzschild coordinates; it is physically meaningless, since it can be eliminated simply by choosing a different coordinate system. An observer falling into a black hole would notice nothing special as he crosses the event horizon.

[xyzt]

I can't do the calculations.

But physics is exactly about being able to do the calculations. You can't be doing physics by cherry-picking quotes from websites. As Markus points out, there is nothing physically particular about the Schwarzschild radius, there are other systems of coordinates that do not exhibit the features that the Schwarzschild system of coordinates exhibits. See for example, the Gullstrand-Painleve system of coordinates.

Edited June 27, 2013 by xyzt

[md65536]

But physics is exactly about being able to do the calculations. You can't be doing physics by cherry-picking quotes from websites. As Markus points out, there is nothing physically particular about the Schwarzschild radius, there are other systems of coordinates that do not exhibit the features that the Schwarzschild system of coordinates exhibits. See for example, the Gullstrand-Painleve system of coordinates.

Thanks.

 

What I mean is I'm unable to answer many of the questions asked due to limited knowledge of the equations. I do understand, I think, that the lengths we're talking about here come from solutions to the Einstein field equations, as they apply to particular observers. In the case of Schwarzschild coordinates, what we're talking about is coordinate length as measured by an ideal observer an infinite distance from the gravitational mass in question.

 

Certainly, someone like myself who doesn't always want to do the maths, must accept that understanding concepts in GR either comes from the maths, or is at least consistent with them. Any of the replies I'm writing, though I realize I make a lot of mistakes, are trying to interpret the meaning of what the maths are saying.

 

There *is* something particular about the Schwarzschild radius... it's the radius at which a mass would collapse due to gravity if all its mass was contained within that radius. However that radius is a coordinate length, and not the same as the coordinate length measured by other observers, and it's not a proper length. Even though it's measured differently in different coordinates, its physical location and physical meaning remains the same... a mass is either a black hole or it isn't, right? Do all observers agree on that?

 

I agree that to get the answers to these questions, (some)one must do the calculations. However to understand the answers, one must understand the meaning of the equations. Without understanding what the equations mean, it's easy for example to calculate the right answer for one observer, but incorrectly assign it to another observer.

 

 

For example, early in the thread you wrote that A and B agree on the distance to the star in the example. This requires understanding that---I think---the distance to which you're referring is expressed in Schwarzschild coordinates, which are the same according to anyone, because they're defined using the measurement frame of an observer at an infinite distance from the mass, not according to (coordinate) measurements made at either A or B using their local coordinates and frame of measurements. This answer (which I'm not yet sure is right, so there is still more for me to understand) doesn't come from the equations, but an understanding of what the equations mean.

Edited June 27, 2013 by md65536

[xyzt]

 

 

There *is* something particular about the Schwarzschild radius... it's the radius at which a mass would collapse due to gravity if all its mass was contained within that radius. However that radius is a coordinate length, and not the same as the coordinate length measured by other observers, and it's not a proper length. Even though it's measured differently in different coordinates, its physical location and physical meaning remains the same... a mass is either a black hole or it isn't, right? Do all observers agree on that?

Yes, all observers agree.

[stefen]

The speed of light in vaccum is 299 792 458 m / s which is the maximum speed of light which which it can travel across the universe.

 

Referrence: http://physics.tutorvista.com/light.html