Varying speed of light in Relativity

[Theoretical]

Maybe someone proficient in Relativity can point out what I'm missing here. According to the equations, time slows down when closer to a massive object. That's from an outsiders perspective since time doesn't change from ones own perspective. Also there's a length contraction closer to a massive object.

 

I haven't found any solid answers regarding any possible change in the speed of light when closer to a massive object. I believe an outside observer sees no change in the speed of light, or does it. So then how is the following example explained. We have light bouncing back and forth between two mirrors. Each time the light reflects there's a click being broadcast so that an observer from a distant location can observe the clicks per second. So time slows down when the mirror device is placed near a massive planet. This means the observer who is far away detects less clicks per second. How is this possible if light is traveling at the same speed unless the mirrors are farther apart? But the mirrors aren't farther apart. According to relativity the mirrors are closer together due to length contraction. So how can the device be producing less clicks per second unless the speed of light decreased? I'm missing something here.

 

BTW there are some discussions on length contraction near a massive object, but there are contradictory posts if the contraction occurs on every axises.

Edited September 26, 2015 by Theoretical

[Mordred]

Yes speed of light is invariant, for all observer's. It appears what your missing is relativity of simultaneity. Ie when the events are observed to occur.

 

"In physics, the relativity of simultaneity is the concept that distant simultaneity whether two spatially separated events occur at the same time is not absolute, but depends on the observer's reference frame."

 

https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity

 

Look at the graphs and the line

 

"Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame."

 

If you send just one signal the signal will occur later or sooner depending on the observer. In other words the two observers won't agree on when the clicks occur.

Edited September 26, 2015 by Mordred

[Theoretical]

Thanks. So I gather that applies to the time between the clicks as well. When the mirror device is away from the massive object, let's say the outside observer detects 1 click every second. When the mirror device is close to the massive object, the outside observer detects 1 click every two seconds. What is the outside observer to think of this? He might be inclined to think that either the spacing between the mirrors increased or the light is traveling slower, or both. But what is happening is that the observer's reference to time becomes increasingly out of sync with the mirror device with each click? When the mirror device is near the massive object the observer detects a click at t=0, t=2, t=4, t=6..., but in reality the clicks occurred at t=x, t=x+1, t=x+2, t=x+3?

[Mordred]

Essentially correct. If you look at the clocks on that link and when the red signal is sent you can see both aspects affected. It's great to try to mathematically seperate each effect but all the effects occur. Dilation, delay in signal and contraction. If you think about that the observer sees all three. Regardless of who the observer is Alice or Bob observing their opposite signal.

Edited September 26, 2015 by Mordred

[Theoretical]

Essentially correct. If you look at the clocks on that link and when the red signal is sent you can see both aspects affected. It's great to try to mathematically seperate each effect but all the effects occur. Dilation, delay in signal and contraction. If you think about that the observer sees all three. Regardless of who the observer is Alice or Bob observing their opposite signal.

Interesting. That creates an even bigger problem for me. Let's say the outside observer is watching the mirror device through a telescope. Each time the light reflects off one of the mirrors, the mirror device produces a bright flash of light for the observer. So as the mirror device remains stationary near the massive object, we are say the observer is detecting only one flash every two seconds, but that's impossible since it means light would have to be traveling slower in order to do that. As stated previously, the observer is becoming increasingly out of sync with the mirror device. So then what happens if the mirror device remains stationary near the massive object for an appreciably long period of time such that the observers out of sync time because so great that the mirror device could travel to the observer is less time? In other words, the mirror device would have traveled to the observer, but the observer would not yet have seen all of the clicks yet.

[Mordred]

Hint what are the units for the speed of light? The length of the meter changes and the measurements of a second changes. So each observer still measures the same speed. Its the units that change not the quantity. Though we can measure the change in wavelength ie redshift.

Edited September 26, 2015 by Mordred

[Theoretical]

Hint what are the units for the speed of light?

Meters / second. I don't see the hint.

 

Hint what are the units for the speed of light? The length of the meter changes and the measurements of a second changes. So each observer still measures the same speed. Its the units that change not the quantity. Though we can measure the change in wavelength ie redshift.

The equation says time slows down. That would mean light must take longer for each reflection. How are you seeing it?

 

Yes, A person that is next to the mirror would of course detect the same amount of time since his detectors would also slow down, but we are talking about a far away observer.

 

Could the missing piece of this puzzle be the effect of leaving such a massive body?

 

One thing we can probably agree that's incorrect is an increasing out of sync with the mirror device.

No?

[Mordred]

The units are measured by coordinates

(x,y,z,ct) GR involves coordinate changes. So Alice and Bob each measure the speed of light using what what he perceives as the units of measure. They will each measure the same speed.

[Theoretical]

The units are measured by coordinates

(x,y,z,ct) GR involves coordinate changes. So Alice and Bob each measure the speed of light using what what he perceives as the units of measure. They will each measure the same speed.

Great, but that doesn't answer my original question. See the mirror example.

[Mordred]

Maybe this will help.

 

 

Lorentz transformation.

 

First two postulates.

 

1) the results of movement in different frames must be identical

2) light travels by a constant speed c in a vacuum in all frames.

 

Consider 2 linear axes x (moving with constant velocity and [latex]\acute{x}[/latex] (at rest) with x moving in constant velocity v in the positive [latex]\acute{x}[/latex] direction.

 

Time increments measured as a coordinate as dt and [latex]d\acute{t}[/latex] using two identical clocks. Neither [latex]dt,d\acute{t}[/latex] or [latex]dx,d\acute{x}[/latex] are invariant. They do not obey postulate 1.

A linear transformation between primed and unprimed coordinates above

in space time ds between two events is

[latex]ds^2=c^2t^2=c^2dt-dx^2=c^2\acute{t}^2-d\acute{x}^2[/latex]

 

Invoking speed of light postulate 2.

 

[latex]d\acute{x}=\gamma(dx-vdt), cd\acute{t}=\gamma cdt-\frac{dx}{c}[/latex]

 

Where [latex]\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[/latex]

 

Time dilation

dt=proper time ds=line element

 

since [latex]d\acute{t}^2=dt^2[/latex] is invariant.

 

an observer at rest records consecutive clock ticks seperated by space time interval [latex]dt=d\acute{t}[/latex] she receives clock ticks from the x direction separated by the time interval dt and the space interval dx=vdt.

 

[latex]dt=d\acute{t}^2=\sqrt{dt^2-\frac{dx^2}{c^2}}=\sqrt{1-(\frac{v}{c})^2}dt[/latex]

 

so the two inertial coordinate systems are related by the lorentz transformation

 

[latex]dt=\frac{d\acute{t}}{\sqrt{1-(\frac{v}{c})^2}}=\gamma d\acute{t}[/latex]

 

So the time interval dt is longer than interval [latex]d\acute{t}[/latex]

[Theoretical]

 

I'm trying to see this through the time dilation equation, which says time slows down from an outside observer's perspective when an object gets closer to a massive object. Therefore, if the clicks per second decrease as measured by the observer, and the distance between the mirrors contracts, then how is that the same speed?

 

The only explanation I see is that the outside observer will not detect any change in the clicks per second.

 

Thanks. I see our post have crossed. I'll analyze your previous post.

 

Ah, i'm referring to *gravitational* time dilation and length contraction. Perhaps that's the difference we're seeing here?

t=tf*sqrt(1 - 2*G*M/(r*c^2))

d=ds*srqt(1 − 2*G*M/(r*c^2))

 

The only explanation I can come up with is that the far away observer will detect the same amount of clicks per second from the mirror device regardless of how close the mirror device is to the massive object. Do you think that's the answer?

[Mordred]

Ah I got what your asking I'm at work atm I'll get back to you later this eve.

Edited September 26, 2015 by Mordred

[Theoretical]

What do you think of this experiment. They did two experiments. The experiment I'm interested in is regarding gravitational time dilation where the optical atomic clock slows down when slightly raised. The only questionable part is where do they take into account the fact that objects higher in elevation rotate faster. My iPhone calculator doesn't have enough precision, so I'll have to do it on my desktop some day to see if their results can be explained by velocity rather then gravitation. An improved experiment would be to move the higher elevated object at an appropriate speed against earths rotation so that it is moving at the scene speed when the clock was lower.

 

http://tf.boulder.nist.gov/general/pdf/2447.pdf

[Mordred]

This eve I'll dig up some papers on gravitational redshift/dilation length contraction.

 

There is a particular article that does a good coverage. Via experiments similar to the one you suggested.

[Theoretical]

This eve I'll dig up some papers on gravitational redshift/dilation length contraction.

 

There is a particular article that does a good coverage. Via experiments similar to the one you suggested.

I've seen those experiments. They're in good agreement with relativity. But that also takes into account the effect of light losing energy due to leaving mass due to gravity, right? While a stationary atomic clock on a massive body doesn't take that into account as far as I see.

[Mordred]

There is also the atomic clock on Everest experiment. Hopefully I can find that paper this eve.

http://www.dailymail.co.uk/sciencetech/article-1314656/Scientists-prove-time-really-does-pass-quicker-higher-altitude.html

 

I read the peer review I'll hunt it down

[Strange]

Not a rigorous experiment, but this is fun: http://www.leapsecond.com/great2005/

http://leapsecond.com/great2005/tour/

Edited September 26, 2015 by Strange

[Theoretical]

There is also the atomic clock on Everest experiment. Hopefully I can find that paper this eve.

http://www.dailymail.co.uk/sciencetech/article-1314656/Scientists-prove-time-really-does-pass-quicker-higher-altitude.html

 

I read the peer review I'll hunt it down

Not a rigorous experiment, but this is fun: http://www.leapsecond.com/great2005/

http://leapsecond.com/great2005/tour/

Thanks. Those are clear well done experiments that shows gravitational time dilation is real. So then what am I missing regarding my mirror experiment? We know that a clock that counts the number times light reflects back and forth between two mirrors will have lower counts if closer to a massive body than if it's far away from the massive body. We know that the distance between the two mirrors does not increase. In fact Einstein's equation says it contracts near the massive object. So if it takes longer from light to travel a shorter distance, then please explain why light is not traveling slower. I fully accept that light is not traveling slower, but I don't see how to explain this. It's probably something so simple and obvious.

[Strange]

Meters / second. I don't see the hint.

 

I haven't read all the posts, but are you missing the fact that because both time and distance change (from the other frame of reference) the result is that the speed of light is constant?

[Theoretical]

I haven't read all the posts, but are you missing the fact that because both time and distance change (from the other frame of reference) the result is that the speed of light is constant?

I know but they change in opposite directions. The distance between the mirrors decreases near the massive body, and there's more time between clicks. But anyhow his post was referring to velocity time dilation, not gravitational. So it's irrelevant.

 

Could the four velocity theory explain what I'm missing? As far as I can tell, if we use only 3 dimensions in explaining the mirror experiment, then it appears light travels slower, but if we use an extra dimension, a 4th dimension if you will, then the light always travels at c. I think this is it!

What do you all think?

https://en.m.wikipedia.org/wiki/Four-velocity

 

So then if it takes light more time to travel between the mirrors, and the mirrors are closer together, then the fourth dimensional vector must increase enough to make up the difference. Correct?

 

Hint what are the units for the speed of light? The length of the meter changes and the measurements of a second changes. So each observer still measures the same speed. Its the units that change not the quantity. Though we can measure the change in wavelength ie redshift.

Yes I get the hint now! Using the 4th dimension balances it all out. Thanks!

 

But hold on, there's more to this, right? This would mean that gravitational time dilation and length contraction only apply in the direction toward the massive body. I've read posts of people saying the same thing, that gravitational length contraction only applies on a certain axis. What do you think?

[pzkpfw]

... but in reality the clicks occurred at ...

I'd avoid using phrases like that. No observers view of the Universe is more "real" than any others. That kind of thinking makes it hard to let go of concepts like absolute time or absolute simultaneity.

[Theoretical]

Hm I think it's back to the drawing board because I'm certain light travels at a slower speed when closer to mass *regardless* if the light is traveling toward or parallel to the mass.

[swansont]

I know but they change in opposite directions. The distance between the mirrors decreases near the massive body, and there's more time between clicks.

 

No, they change in the same direction. The clock runs slow; it registers less time passing relative to a clock far away from the mass.

What do you think of this experiment. They did two experiments. The experiment I'm interested in is regarding gravitational time dilation where the optical atomic clock slows down when slightly raised. The only questionable part is where do they take into account the fact that objects higher in elevation rotate faster.

 

They ignored it.

 

1 meter increase in radius is 6.28 meters increase in circumference. 86400 sec/day; that's ~10^-5 m/sec, so v/c is of order 10^-13. Kinematic term varies as v²/c² so that's 10^-26, or 9-10 orders of magnitude smaller than what they measured. Nothing questionable about it.

[Mordred]

Hm I think it's back to the drawing board because I'm certain light travels at a slower speed when closer to mass *regardless* if the light is traveling toward or parallel to the mass.

You need to drop the idea light travels slower. Think in terms of coordinate change due to space time curvature.

 

Remember postulate 1.

 

I found a handy simulator that you can play around with.

 

 

http://www.adamtoons.de/physics/gravitation.swf

 

It may require plugins of your using a phone.

 

Now remember time always run slower in a gravity well than the clock outside of the well. This both observers Alice and Bob agree on. Which is slightly different than inertial frame time dilation.

 

if the clock stays at the same gravitational potential it's clock will maintain the same rate which is slow to Alice at Euclidean space.

 

If you think about redshift/blueshift you can make the connection between the two scenarios.

 

[latex]\frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}[/latex]

 

So light is bluedshifted when it falls into the well ,redshifts when it climbs out. Time and length contraction follow the same relation.

 

By the formulas you posted.

 

[latex]t_o=t_f\sqrt{1 - \frac{2GM}{r c^2}}[/latex]

 

[latex]d=ds\sqrt{1 - \frac{2GM}{r c^2}}[/latex]

Wiki has the formula for circular orbits including a graph

 

https://en.m.wikipedia.org/wiki/Gravitational_time_dilation

Edited September 27, 2015 by Mordred

[Theoretical]

You need to drop the idea light travels slower. Think in terms of coordinate change due to space time curvature.

 

Remember postulate 1.

 

I found a handy simulator that you can play around with.

 

 

http://www.adamtoons.de/physics/gravitation.swf

 

It may require plugins of your using a phone.

 

Now remember time always run slower in a gravity well than the clock outside of the well. This both observers Alice and Bob agree on. Which is slightly different than inertial frame time dilation.

 

if the clock stays at the same gravitational potential it's clock will maintain the same rate which is slow to Alice at Euclidean space.

 

If you think about redshift/blueshift you can make the connection between the two scenarios.

 

[latex]\frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}[/latex]

 

So light is bluedshifted when it falls into the well ,redshifts when it climbs out. Time and length contraction follow the same relation.

 

By the formulas you posted.

 

[latex]t_o=t_f\sqrt{1 - \frac{2GM}{r c^2}}[/latex]

 

[latex]d=ds\sqrt{1 - \frac{2GM}{r c^2}}[/latex]

Wiki has the formula for circular orbits including a graph

 

https://en.m.wikipedia.org/wiki/Gravitational_time_dilation

Okay then that means you the speed of light makes no sense in terms of Relativity. Don't you see my point? Again:

 

The mirror experiment is a clock. If we send the mirror device near a massive planet for some time, then when it returns it lost time. This means that if we have the mirror device emitting a signal every time the light beam reflects off a mirror that the far away observer will see less emitted signals per second because the mirror clock is running slower. And this will be verified when the mirror device comes back to the observer. Also, according to relativity the distance between the mirrors decreases when near the massive planet. Therefore don't you see that if it takes light longer to travel from one mirror to the other mirror, and the distance is less, that the light is traveling slower. Yes initially I saw a way out of this puzzle with the Four speed theory, but that doesn't seem to explain this because we know from experiments that the atomic clocks do not have to positioned in some preferred axis.