Is the Speed of Light Bidirectional in an Expanding Universe?

[Tracer]

Is the average nonlocal speed of light the same for travel out from the Sun and travel back to the Sun over the distances the Voyagers are now located?

 

[davenn]

Is the average nonlocal speed of light the same for travel out from the Sun and travel back to the Sun over the distances the Voyagers are now located?

Yes

Is there a reason why you think it wouldn't be ?

 

[Tracer]

Yes

Is there a reason why you think it wouldn't be ?

No, I believe it does change by its amount of energy lost or gained as it moves through the sun's gravitational field. I believe the amount of speed change should be equal to the difference in the value of the escape velocity at any distance from the Sun and the value of the escape velocity at either extreme of the EMR's motion away from ot back to the Sun.

 

[Nugatory]

This question is much trickier than it appears to be.

Presumably by "non-local speed of light" you mean what we get when you divide the distance traveled by the time in flight? That's how we generally define the speed of something: distance divided by time needed to cover the distance.

However, to calculate the speed of the outbound signal we must know what time it is on Earth when the light signal reaches its remote destination; without this we have no way of knowing how much time passed between when the signal left Earth and when it was received. Likewise, it's easy for us to know what time the inbound signal arrives at Earth - but that doesn't tell us the flight time because we don't know when the signal was emitted.

Thus, to calculate this non-local speed (the technical term would be "coordinate speed" and you'll find many discussions of it in other threads here) we need some rule (called a "simultaneity convention") for saying "at the same that a clock on Earth reads X a clock at the remote destination reads Y". However, in curved spacetime with noticeable gravitational effects there is no single right rule for doing this. The simultaneity convention can be chosen more or less arbitrarily, and depending on this choice we can make the inbound and outbound coordinate speeds come out to pretty much whatever we want.

We can choose coordinates in which the speeds come out as you suggest. However that's not telling us anything about the behavior of light, it's just telling us that we've made an arbitrary choice about how we're relating times in different places that made the numbers come out that way. That choice may be very convenient for some particular observer, but it's still arbitrary.

On the other hand, there are things that hold true no matter how we make these arbitrary choices. For example, the out-and-back round-trip time for a light signal can be calculated from the readings on a single earthbound clock, no arbitrary choice required. Likewise, the amount by which the light will be blue-shifted or red-shifted is a fact unaffected by our choice of coordinates and simultaneity convention. Things like that are called "invariants" and generally have real physical significance.

 

[Tracer]

On the other hand, there are things that hold true no matter how we make these arbitrary choices. For example, the out-and-back round-trip time for a light signal can be calculated from the readings on a single earthbound clock, no arbitrary choice required. Likewise, the amount by which the light will be blue-shifted or red-shifted is a fact unaffected by our choice of coordinates and simultaneity convention. Things like that are called "invariants" and generally have real physical significance.

My interest is in the method used to determine the relative speed of NASA's Voyagers with the Earth. I have been led to believe that is accomplished by a EMR pulse generated on the Earth and directed to a Voyager. A transponder on the voyager retransmits a pulse with the received pulse frequency within microseconds of its receipt back to the Earth where the Earth's motion and position changes during the two way trip is removed from the determination of the Voyager's speed and distance relative to the Earth. How can Voyager's speed relative to the Earth be determined if the Doppler Effect on the pulse from Earth and the Voyager is unaffected by Energy loss or gain as it travels through the Suns's gravitational field? And if the Coordinate Speed of light, (My reference to a nonlocal measurement of light speed at a distance from the Earth) does not change, then the distance between the Voyager and the Earth will be incorrect. In essence, the Voyagers will neither be at the distance NASA determines them to be nor will they be moving radially relative to the Earth as NASA determines them be if based on the locally measured elapsed time between the Earth's generaton of a EMR pulse and the receipt of the voyager's transponder pulse. Perhaps. I have misinterpretated your response. I am willing to learn.

 

[phyzguy]

The Doppler effect does not change the speed at which light travels. It only changes the frequency and wavelength of the EM wave.

 

[Tracer]

The Doppler effect does not change the speed at which light travels. It only changes the frequency and wavelength of the EM wave.

phyzguy, of coarse a Doppler Effect doesn't change anything. It is just an indication that an EM source has either gained or lost energy during its travel from its source to an observer, or alternately the EM source has a non-zero motion relative to an observer.
At a distance of about 14 billion light years from an observer on the Earth, space is expanding due to Hubbel Expansion at the speed of c (2.99792458E08 meters/second. Since EM sources at that distance are entrained in that expanding space, they and any EM they emit also will move away from an Earth observer at the speed of c. Consequently, no EM from cosmic objects at or beyond 14 billion light years will be able to reach the Earth. Granted that those same objects can be seen on Earth if they transmitted some light before they reached the 14 BLY boundary. However, those objects will be seen where they were located many years ago.
However, even though no EM can be observed from objects at a distance of 14 BLY, the Speed of EM relative to the Earth emitted by those objects can be calculated as a function of the escape velocity at their location.

 

[phyzguy]

phyzguy, of coarse a Doppler Effect doesn't change anything. It is just an indication that an EM source has either gained or lost energy during its travel from its source to an observer, or alternately the EM source has a non-zero motion relative to an observer.
At a distance of about 14 billion light years from an observer on the Earth, space is expanding due to Hubbel Expansion at the speed of c (2.99792458E08 meters/second. Since EM sources at that distance are entrained in that expanding space, they and any EM they emit also will move away from an Earth observer at the speed of c. Consequently, no EM from cosmic objects at or beyond 14 billion light years will be able to reach the Earth. Granted that those same objects can be seen on Earth if they transmitted some light before they reached the 14 BLY boundary. However, those objects will be seen where they were located many years ago.
However, even though no EM can be observed from objects at a distance of 14 BLY, the Speed of EM relative to the Earth emitted by those objects can be calculated as a function of the escape velocity at their location.

What does this have to do with the Voyager probes, which are about 0.002 light-years away?

 

[Tracer]

phyzguy, Look again at post #5 in this thread.

 

[phyzguy]

phyzguy, Look again at post #5 in this thread.

My point is that cosmological issues like you refer to in post #7 have no relevance when you are talking about a nearby object like the Voyager probes. Hubble expansion does not operate at these scales, and even if it did, the magnitude would be negligibly small.

 

[Tracer]

I agree that the Voyagers have not yet reached the distance at which the Dark Energy force would prevail over the combined attractive forces of Baryonic and Dark matter. I believe a discussion of what happens after that distance is exceeded should be the subject of another thread. Inthe meantime, I will accept that that the speed of light has the same coordinate (my non-local) speed both ways between the Earth and the Voyagers. Are there any observations or experiments which indicate that is correct?

 

[Nugatory]

Mentors' note: This thread has been moved from General Physics to the relativity subforum

 

[Tracer]

My OP questioned the average speed of EM separately for each direction between the Earth and the voyagers. In the ensuing discussions I mentioned Hubbel Expnsion which causes at a distance of about 13.77 Billion light years, the speed of EM transmitted from a object toward the Earth to become zero meters per second and the speed of EM transmitted directly away from the Earth to become the constant value of 2c. (plus or minus any peculiar motion of the Object) I admitted that Hubell expansion does not occur at the present distance of the voyagers. I believe Hubbell expansion does not occur for objects at distances less than about 1.3338E18 meters from the Sun. Only at that distance does the repulsive force of Dark Energy become greater than the combined attractive forces of Baryonic and Dark Matter. I would like to discuss in this forum, how the non-local (Your Coordinate ) speed of EM changes for objects subject to Hubbell expansion as a function of the Escape velocity at their distance from the Sun. If this is not permitted in this Forum, Delete my post and I will say nothing more regarding this topic.

 

[Janus]

No, I believe it does change by its amount of energy lost or gained as it moves through the sun's gravitational field. I believe the amount of speed change should be equal to the difference in the value of the escape velocity at any distance from the Sun and the value of the escape velocity at either extreme of the EMR's motion away from ot back to the Sun.

Light expresses its loss or gain of energy as a decrease or increase in frequency as it climbs out off or falls into a gravity field, not by changing its velocity.
However, even if this were not the case and it did pick up speed falling in like a physical mass, that increase in speed would be nowhere near the magnitude of escape velocity.
For an object falling, it total energy KE+PE remains constant. This works to be
$$E = \frac{mv^2}{2}- \frac{GMm}{r}$$
where GM is the gravitational parameter for the Sun in this case
v the velocity of the object relative to the Sun
m the mass of the object
r the distance of the object from the Sun.
Ignoring Relativity for the moment, assume that you have a 1 kg object starting at a infinite distance from the Sun and traveling at 300,000,000 m/s(~c)towards it.
with r equal to infinity, it total energy is equal to just its kinetic energy or 4.5e16 joules.
When it reaches Earth orbit distance from the Sun it total energy must be the same, so we can say

$$4.5e16 J = \frac{mv^2}{2}- \frac{GMm}{r}$$
GM= 1.3275e20m^3/s^2
r= 1.496e11m
and m = 1 kg
solving for v, we get
300,000,003 m/s
It will only have picked up ~3 m/s during its inward fall.
This is a fair bit short of the 42,000 m/s that is the escape velocity at Earth orbit distance.
Neither Voyager is infinitely distant, so the speed gained falling with a starting velocity near c would be even less.
It is even quite a bit less that the better than 15,000 m/s that the probes are traveling. Any correction to the measured speed of the Voyager craft due to this effect would be very small.

 

[Tracer]

This thread had been moved to relativity discussions because I am now asking how the speed of light relative to the Earth is affected when the source of the light is at a distance where Hubbell space expansion is c or near c. I am not interested in what an observer on either the Earth or the distant object would measure the speed of light to be at their locations. Instead, what and how would an Earth observer determine (Calculate) the initial relative speed with the Earth of a pulse of light made on the distant object ?

 

[jbriggs444]

This thread had been moved to relativity discussions because I am now asking how the speed of light relative to the Earth is affected when the source of the light is at a distance where Hubbell space expansion is c or near c. I am not interested in what an observer on either the Earth or the distant object would measure the speed of light to be at their locations. Instead, what and how would an Earth observer determine (Calculate) the initial relative speed with the Earth of a pulse of light made on the distant object ?

First you would have to define what you mean by "initial relative speed with the Earth". It depends on the coordinates you use. There is no underlying truth of the matter.

 

[Tracer]

First you would have to define what you mean by "initial relative speed with the Earth". It depends on the coordinates you use. There is no underlying truth of the matter.

define :"The Initial relative velocity with the earth" as the relative speed, determined by an Earth observer, at the time of creation of an EM pulse by a distant object . The object creating the EM pulse must be at a distance at which Hubbell space expansion is occurring. Use a distance of 10.0 light years if you want a specific distance. I asked for the "Initial RV" because as that pulse moves toward the earth, it will be moving into positions in which the Hubbell expansion is less than at the point of initial creation and therefore the RV with the Earth will increase. Since the EM pulse transit time is affected by the expansion rate of space, it appears that the EM relative velocity with Earth will change as it moves toward the Earth.

 

[Ibix]

define :"The Initial relative velocity with the earth" as the relative speed, determined by an Earth observer,

How are you measuring speed? Rate of change of distance, presumably, but do you mean angular diameter distance? Luminosity distance? Co-moving distance? Some other measure of your own devising? You'll get different answers depending which one you pick. As @jbriggs444 says, there isn't a unique answer to your question.

Use a distance of 10.0 light years if you want a specific distance.

Try 10Mpc at minimum.

Since the EM pulse transit time is affected by the expansion rate of space, it appears that the EM relative velocity with Earth will change as it moves toward the Earth.

That depends on how you define velocity. There isn't a single unambiguous definition.

 

[phyzguy]

define :"The Initial relative velocity with the earth" as the relative speed, determined by an Earth observer, at the time of creation of an EM pulse by a distant object . The object creating the EM pulse must be at a distance at which Hubbell space expansion is occurring.

Think about what you are asking. An object 1 billion light years away emits a pulse of EM radiation. You are asking, what is the speed of this EM pulse according to an observer here on Earth. How could you possibly make such a measurement? How could the observer on Earth even know that the EM pulse was emitted?

 

[sweet springs]

Instead, what and how would an Earth observer determine (Calculate) the initial relative speed with the Earth of a pulse of light made on the distant object ?

Increase of distance of the two bodies on inflating universe per universal time can be more than c. However, it is not called as velocity or speed in TOR.

 

[jbriggs444]

Increase of distance of the two bodies on inflating universe per universal time can be more than c. However, it is not called as velocity or speed in TOR.

It is also not a well-defined quantity without further stipulations on exactly how it is to be calculated. In particular, a foliation is needed to establish a definition of "universal time".

 

[Grinkle]

how would an Earth observer determine (Calculate) the initial relative speed with the Earth of a pulse of light made on the distant object ?

There are some threads in the forums about one-way speed of light that might be helpful, if you do a search you will find them.

Here is one that has some more discussion on co-ordinate dependency - I know you specifically said calculate and not measure, I am referring you to the parts of the discussion on co-ordinates.

https://www.physicsforums.com/threa...-measuring-the-one-way-speed-of-light.951761/

 

[Dale]

I would like to discuss in this forum, how the non-local (Your Coordinate ) speed of EM changes

The coordinate speed of light is not constrained for non inertial coordinates. It is only inertial coordinates which require that the coordinate speed of light be c.

For non inertial coordinates the equivalent statement is that light travels on null geodesics. In inertial frames a null geodesic moves at c in a straight line, so the general statement covers the inertial case also.

 

[Tracer]

Think about what you are asking. An object 1 billion light years away emits a pulse of EM radiation. You are asking, what is the speed of this EM pulse according to an observer here on Earth. How could you possibly make such a measurement? How could the observer on Earth even know that the EM pulse was emitted?

Obviously, an Earth observer will not know that a distant object has emitted a pulse of light until the pulse reaches the Earth and is observed there. There seems to be a method of calculating the relative speed of the light pulse with the Earth at the time the pulse was created. The method requires that the distance from the Earth to the pulse emitting object can be determined. Astronomers now use a type of super novae which have a known light emission pattern to determine their distance from the earth. This is accomplished by how much diminished the light intensity from the object has become over its travel to the Earth. If that distance is expressed in kilometers per mega parsec, then multiply that distance by an accepted value of Hubbells Constant to determine the expansion rate of space in kilometers per second relative to the earth. Finally subtract that relative velocity from the value of c (2.99782458E05 km/second) to determine the relative velocity of the pulse with the Earth at the distance of the object from the Earth at the time the pulse was created.

 

[Dale]

I have no idea what you described there. In curved spacetime and non inertial frames all you can say is that light follows a null geodesic. This captures the physical meaning of the invariance of c in a coordinate independent way.

 

[PeterDonis]

Astronomers now use a type of super novae which have a known light emission pattern to determine their distance from the earth.

What they are determining is not the "ruler distance" that you are implicitly thinking, nor is it the coordinate distance. It is the "luminosity distance", i.e., the observed luminosity, compared with the (assumed known based on the light emission pattern) source luminosity, converted into distance units for convenience. The actual relationship between luminosity distance and ruler distance (or coordinate distance) depends on the expansion history of the universe; it is not something you can know independently.

 

[phyzguy]

Obviously, an Earth observer will not know that a distant object has emitted a pulse of light until the pulse reaches the Earth and is observed there. There seems to be a method of calculating the relative speed of the light pulse with the Earth at the time the pulse was created. The method requires that the distance from the Earth to the pulse emitting object can be determined. Astronomers now use a type of super novae which have a known light emission pattern to determine their distance from the earth. This is accomplished by how much diminished the light intensity from the object has become over its travel to the Earth. If that distance is expressed in kilometers per mega parsec, then multiply that distance by an accepted value of Hubbells Constant to determine the expansion rate of space in kilometers per second relative to the earth. Finally subtract that relative velocity from the value of c (2.99782458E05 km/second) to determine the relative velocity of the pulse with the Earth at the distance of the object from the Earth at the time the pulse was created.

I don't know what level you are at in your studies, but the concept of distance in an expanding spacetime is not a simple concept. I found this paper by David Hogg to be an excellent summary of the different distance measures. If this is too advanced, it might at least give you an idea of the different distance measures that exist.

 

[Tracer]

What they are determining is not the "ruler distance" that you are implicitly thinking, nor is it the coordinate distance. It is the "luminosity distance", i.e., the observed luminosity, compared with the (assumed known based on the light emission pattern) source luminosity, converted into distance units for convenience. The actual relationship between luminosity distance and ruler distance (or coordinate distance) depends on the expansion history of the universe; it is not something you can know independently.

Please consider a universe without curvature, at least to start.

Wouldn't the expansion history of the potion of the universe through whixh the distant object traveled, be contained along the parh EM took from its source to rhe earth? And if gravitational fields are -conservative, wouldn't only the difference ot endpoints matter? If that is correct, couldn't an Earth observer attribute the entire Doppler shift of spectrographic lines to the motion of the distant source and thereby determine the RV of expanding space with the earth?

 

[Nugatory]

Please consider a universe without curvature, at least to start...the expansion history ... gravitational...

Gravity and expansion are both curvature effects - if you're considering either of these you are necessarily considering a universe with non-zero curvature.

Be aware that even in a flat universe (no curvature, no gravity, no expansion) it is impossible to measure the one-way speed of light; the best we can do is measure the round-trip time and assume that the speed on the inbound and outbound legs is the same. Any experiment that purports to measure the one-way speed of light will, upon closer examination, turn out to include hidden assumptions that are equivalent to assuming that the one-way speed is equal to the two-way speed. (We have several older threads on this issue).

If that is correct, couldn't an Earth observer attribute the entire Doppler shift of spectrographic lines to the motion of the distant source

Yes, but...

and thereby determine the RV of expanding space with the earth?

The key word here is "attribute". Yes, if I choose to attribute all the Doppler shift to recession then I can calculate a coordinate velocity for distant galaxies. However, when I made that choice I was also choosing to use a particular coordinate system (one that happens to be very convenient for cosmologists on earth, which is why we use it) so the coordinate velocity that I come up with has no particular physical significance. Use different coordinates and we'd come up with a different coordinate velocity and not all the redshift would be attributed to expansion.

 

[Tracer]

The key word here is "attribute". Yes, if I choose twilltribute all the Doppler shift to recession then I can calculate a coordinate velocity for distant galaxies. However, when I made that choice I was also choosing to use a particular coordinate system (one that happens to be very convenient for cosmologists on earth, which is why we use it) so the coordinate velocity that I come up with has no particular physical significance. Use different coordinates and we'd come up with a different coordinate velocity and not all the redshift would be attributed to expansion.

I don't believe that I can say anything more without getting banned from this forum. Therefore, I will post nothing more on this thread. My thanks to those who tried to help me understand their methods.

 

[PeterDonis]

f gravitational fields are -conservative

They aren't in an expanding universe. More precisely, in an expanding universe, the concept of "gravitational field" is not well-defined.

 

[Tracer]

They aren't in an expanding universe. More precisely, in an expanding universe, the concept of "gravitational field" is not well-defined.

Thank you. Your comments have been noted.