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e2m2a
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Does a photon gain speed if it travels in "free-fall" toward the earth? A particle of mass gains speed as it free-falls to the earth, and yet, mass is just another form of energy. Light is energy. So, does light gain speed?
In the case of Earth we can use the Schwarzschild solution as an approximation, in this case, in Schwarzschild coordinates, the coordinate speed of light actually slows down the closer it gets to the Earth. This is not only true for light but for all objects that have a coordinate velocity above a critical speed of:e2m2a said:Does a photon gain speed if it travels in "free-fall" toward the earth? A particle of mass gains speed as it free-falls to the earth, and yet, mass is just another form of energy. Light is energy. So, does light gain speed?
e2m2a said:Does a photon gain speed if it travels in "free-fall" toward the earth? A particle of mass gains speed as it free-falls to the earth, and yet, mass is just another form of energy. Light is energy. So, does light gain speed?
e2m2a said:Therefore, wouldn't it be correct for the observer on the Earth to conclude that the speed of the photon increased relative to the Earth observer's frame?
Passionflower said:I suspect you will get probably 10 postings that will only give you information about the speed of light measured locally, which is always c. But of course people deserve more information.
In the case of Earth we can use the Schwarzschild solution as an approximation, in this case, in Schwarzschild coordinates, the coordinate speed of light actually slows down the closer it gets to the Earth. This is not only true for light but for all objects that have a coordinate velocity above a critical speed of:
[tex]
3^{-1/2}
[/tex]
This is also the case for the proper velocity (e.g. the velocity wrt local shell observers) but in this case the critical velocity is
[tex]
2^{-1/2}
[/tex]
You seem to have the impression that nothing physical can be calculated from using the Schwarzschild solution. If that is so then you are completely wrong.PAllen said:Curious what you think these speeds mean.
Mentz114 said:the photon will gain energy, exactly equivalent to the amount it would have gained if it's speed had increased through falling. But the energy gained is in the increase in frequency, not speed, which is constant.
Passionflower said:You seem to have the impression that nothing physical can be calculated from using the Schwarzschild solution. If that is so then you are completely wrong.
If you pay attention I and a few others constantly use the Schwarzschild solution to make physical meaningful calculations on this forum. But I have not seen one single calculation from you using the Schwarzschild solution, or any other solution for that matter, all you seem to do is criticize those who actually do make the effort here.
Curious why you are at all interested in GR if you never want to do any calculations.
I certainly could make physically meaningful calculations about what I wrote above or quote several papers that discuss this situation. If you cannot, then if you want to learn about GR, I strongly suggest you are going to start making an effort. Looking at GR from a 30,000ft height and thinking you know it all without being able to do even simple calculations using the Schwarzschild solution is in my opinion being in a state of delusion.
From the information you give it is very easy to calculate the physical distance and roundtrip time (both in proper time for R2 and R3's clock) in terms of R.PAllen said:Assumming R is the event horizon radius, and a worldline of an observer maintaining fixed position 2R, and another world line at e.g. 3R, what speed of light would be measured between them? For me, this would immediately raise the question of what points of the world lines to consider simultaneous, because I can't conceive of measuring distance without this, and can't see how to measure speed without measuring distance.
It is very easy to calculate the coordinate time in terms of R and from this you can calculate the proper time both for R2 and R3.PAllen said:This would immediately put me in a quandary. I would attach no meaning to coordinate time.
Another good reason to actually make the calculations and plot them for various actual values of R. If you do that you will find out that you are wrong calling those observers *extremely* non-inertial observers. How 'non inertial' really depends on the actual value of R. For instance if R is very large the proper acceleration of the stationary observers could be much smaller than 1g. Also in another calculation I made last week on this forum I demonstrated that those observers would not exactly correspond to Rindler observers. Also this calculation is trivial, we can immediately calculate the difference from Rindler acceleration in terms of R.PAllen said:For one thing, both of these world lines are *extremely* non-inertial observers (think of the rocket g forces required to mainain constant position; barring tidal effects, they would correspond to Rindler observers with very high G, different for each world line; time would run very differently for each world line.).
Both yuiop and I have made similar calculations and by using prior postings you can obtain the correct formulas on how to calculate this situation. Basically all you need is the integrated distance between R2 and R3, the integrated coordinate time light takes to go from R2 and R3 and vice versa and on how to convert this time to proper time for both R2 and R3. Again, this is another good example why it is very important to do exercises, both yuiop and I went through these issues but you do not seem to realize it, and the reason I expect is that you have not tried the calculations yourself.PAllen said:I don't know whether Passionflower has gone through this exercise or not, but I don't see such issues even being mentioned.
I do not see how Born rigidity is relevant when we want to measure the roundtrip speed of light between two stationary points.PAllen said:For me, I wouldn't see how to use Born rigidity either.
Again measuring the distance and roundtrip speed of light, in proper time for both endpoints R2 and R3 is trivial and unambiguous.PAllen said:So I would be completely stumped by how to compute what GR predicts for this measurement, but I would at least feel I have asked relevant starting questions.
PAllen said:Getting back to something like the original question on this post, the way I would set up the problem would be:
Assumming R is the event horizon radius, and a worldline of an observer maintaining fixed position 2R, and another world line at e.g. 3R, what speed of light would be measured between them?
For me, this would immediately raise the question of what points of the world lines to consider simultaneous, because I can't conceive of measuring distance without this, and can't see how to measure speed without measuring distance.
This would immediately put me in a quandary. I would attach no meaning to coordinate time.
Passionflower said:From the information you give it is very easy to calculate the physical distance and roundtrip time (both in proper time for R2 and R3's clock) in terms of R.
Both yuiop and I have done similar calculations in various topics. This time I really leave it as an exercise to calculate it, it is straightforward and in no way ambiguous.
Round trip time is in R2's proper time, for example, is straightforward. For distance, a pair of events considered simultaneous is required to do it any invariant way. What points on the the two world lines should be considered simultaneous?Passionflower said:From the information you give it is very easy to calculate the physical distance and roundtrip time (both in proper time for R2 and R3's clock) in terms of R.
Both yuiop and I have done similar calculations in various topics. This time I really leave it as an exercise to calculate it, it is straightforward and in no way ambiguous.
Passionflower said:Another good reason to actually make the calculations and plot them for various actual values of R. If you do that you will find out that you are wrong calling those observers *extremely* non-inertial observers. How 'non inertial' really depends on the actual value of R. For instance if R is very large the proper acceleration of the stationary observers could be much smaller than 1g. Also in another calculation I made last week on this forum I demonstrated that those observers would not exactly correspond to Rindler observers. Also this calculation is trivial, we can immediately calculate the difference from Rindler acceleration in terms of R.
Passionflower said:Basically all you need is the integrated distance between R2 and R3, the integrated coordinate time light takes to go from R2 and R3 and vice versa and on how to convert this time to proper time for both R2 and R3.
Born rigidity would provide a possible answer, without relying on light, to define which events at R2 and R3 could be considered simultaneous by an observer at R2.Passionflower said:I do not see how Born rigidity is relevant when we want to measure the roundtrip speed of light between two stationary points.Again measuring the distance and roundtrip speed of light, in proper time for both endpoints R2 and R3 is trivial and unambiguous.
Yes, that would be much easier. I was trying to accentuate a hypothetical possibility you would measure something different from c in trip up and down the gravity well. I was aiming to see if you could define a measurment over a span where flatness cannot be assumed.pervect said:What I would suggest is to measure the speed between points that are closer together, i.e between 2R and 2.0001R, or more generally between R' and R'+epsilon.
I am familiar with this issue and choosing to ignore it. But even for a two way measurement of lightspeed, you first have to come up with a distance, which seems to require simultaneity, which I couldn't solve, and still don't understant how to solve for a distance like 2R to 3R.pervect said:The problem of not being able to measure the one-way speed of light without defining how to syncrhronize clocks is a problem left over from special relativity. It has various resolutions - the most common is to measure the round trip speed, and state that you are explicitly assuming isotropy, so that the time is equal forwards and backwards.
Technically, nowadays, the speed of light is defined as a constant. So if you're actually measuring the speed of light, you probably should note that you're using a physical standard meter rod as your reference.
pervect said:This then gives the question of what mathematical model to use for your physical meter rod - since you are calculating the result rather than performing the experiment. Born rigidity immediately comes to mind, and would be my suggestion. Basically you can figure out the expected stretch in your actual physical meter rod due to the stresses on it, and either call them experimental error, or make a note of how big they are and say that you are compensating for them.
pervect said:In general coordinate anything doesn't have any particular physical meaning, unless one chooses the coordinates correctly. In the Schwarzschild geometry it happens to have some significance as a killing vector.
Ok, so we have a Schwarzschild radius of R and two stationary observers R2 and R3.PAllen said:Assumming R is the event horizon radius, and a worldline of an observer maintaining fixed position 2R, and another world line at e.g. 3R, what speed of light would be measured between them?
Passionflower said:Ok, so we have a Schwarzschild radius of R and two stationary observers R2 and R3.
Then the ruler distance between them is:
[tex]
\rho = R \left( \sqrt {3}\sqrt {2}-\sqrt {2}+\ln \left( -\sqrt {3}+\sqrt {3}
\sqrt {2}-\sqrt {2}+2 \right) \right)
[/tex]
Events? What events?PAllen said:This is the key point. Which events are 2R and 3R are used to calculate this? That I what I am asking about (as was Pervect). Given an answer to this, a calculation is easy, but what criterion is used? If one rules out using a light based definition of simultaneity (else circularity for this problem) and Born rigidity (because you don't have approximate flatness), then what do you use? I hope there is a good answer, but you haven't given it.
Passionflower said:Events? What events?
I provided the calculations of the ruler distance and the radar distance both for coordinate and proper time between two stationary observers.
For example, the Schwarzschild coordinate r can in principle be determined by measuring the Kretschmann invariant, and the Schwarzschild coordinate t can then in principle be determined by transporting a clock to the appropriate location along a radial path from some reference point and using the Schwarzschild metric to connect the clock time to the Schwarzschild t coordinate, based on the clock's known trajectory (measured in the form of r as a function of proper time).Passionflower said:In the case of Earth we can use the Schwarzschild solution as an approximation, in this case, in Schwarzschild coordinates, the coordinate speed of light actually slows down the closer it gets to the Earth.
One stationary space station, a known distance from the surface of a planet, could calculate the ruler distance to another stationary space station by measuring the round trip time of light, from the elapsed proper time he could derive the ruler distance by calculating the coordinate speed of light using Schwarzschild coordinates.bcrowell said:The next question is whether the statement is of any physical interest. I don't see any reason to think that it is. It refers to a coordinate velocity, and in general coordinate velocities are of no physical interest.
Passionflower said:One stationary space station, a known distance from the surface of a planet, could calculate the ruler distance to another stationary space station by measuring the round trip time of light, from the elapsed proper time he could derive the ruler distance by calculating the coordinate speed of light.
Passionflower said:One stationary space station, a known distance from the surface of a planet, could calculate the ruler distance to another stationary space station by measuring the round trip time of light, from the elapsed proper time he could derive the ruler distance by calculating the coordinate speed of light using Schwarzschild coordinates.
Different positions in the same orbit?PAllen said:The difficulty I have with this is the coordinate speed of light. Whose? Consider 2 cases: two space stations stationary relative to each other by being in different positions on the same orbiot; two stations under power, held stationary above the Earth as if it weren't rotating. Each of these observer would be quite different frames of reference, and the Swarzchild coordinate speed of light would not seem to have relevance to either of these scenarios.
Passionflower said:Let me cut this short: do you think my calculations are right or wrong?
If they are wrong please say what you think is wrong and provide the right answer.
If they are right we are done.
There is no point in arguing with people who keep on going on about 'it is not defined', 'it is too hard', 'define it', 'it depends' and who never bother to write a single formula or do one single calculation, then when you confront them with hard formulas and answer they neither confirm nor deny it is right or wrong, they simply ignore the work and go on as they did before. Perhaps some of those 'high level' folks should take the famous 'shut up and calculate' saying to heart.
e2m2a said:Does a photon gain speed if it travels in "free-fall" toward the earth? A particle of mass gains speed as it free-falls to the earth, and yet, mass is just another form of energy. Light is energy. So, does light gain speed?
That is not naive at all, in fact the poster is totally correct.bcrowell said:The OP naively imagined that the question had a definite answer without regard to any specific coordinate system. The helpful way to answer the OP's question was to point out that the question was ill-defined.
I don't think it's really right to say that using rulers and proper times makes something "coordinate free". After all, inertial coordinate systems are typically defined in terms of a set of rulers and synchronized clocks...anything that allows you to assign a position and a time to any arbitrary event can be treated as defining a coordinate system. (and if two people describe definitions of distances and times using the exact same system of rulers and clocks, but the first uses the words says that the readings on the rulers and clocks define the 'coordinates' of events while the second just talks about 'distances' and 'times', then surely this mere difference in wording does not mean the first is giving a coordinate-dependent description of events while the second is giving a coordinate-independent description)Passionflower said:That is not naive at all, in fact the poster is totally correct.
Below is a plot of light speeds between pairs of static observers (o1, o2) separated a fixed ruler distance of 1 as measured by a clock at observer o1. In the plot you can see the ruler distance (which is 1 for each pair) divided by the radar distance, this ratio is larger for pairs closer to the EH. This is a coordinate free plot as only the ruler distance and proper time is used.
So you are claiming that ruler distance and radar distance as measured by a clock for static observers depend on the chosen coordinate chart in a Schwarzschild solution?JesseM said:I don't think it's really right to say that using rulers and proper times makes something "coordinate free". After all, inertial coordinate systems are typically defined in terms of a set of rulers and synchronized clocks...anything that allows you to assign a position and a time to any arbitrary event can be treated as defining a coordinate system. (and if two people describe definitions of distances and times using the exact same system of rulers and clocks, but the first uses the words says that the readings on the rulers and clocks define the 'coordinates' of events while the second just talks about 'distances' and 'times', then surely this mere difference in wording does not mean the first is giving a coordinate-dependent description of events while the second is giving a coordinate-independent description)
No, I just say that any definition of distances and times in terms of rulers and clocks can itself be taken as a definition of a coordinate system; in fact, the only physical way to define any coordinate system is in terms of some set of physical rulers (or other physical distance measures like radar distance) and physical clocks. Do you agree that textbooks (following the example of Einstein's original 1905 paper) typically define inertial coordinate systems in such a physical way too, by picturing a network of rigid rulers and synchronized clocks like the one illustrated here? If so, would you say this somehow means that statements about "velocity" in such a system of rulers and clocks are "coordinate independent"? I would say the only coordinate-independent statements about such a system are purely local ones like "object A was next to marking x=5 on the ruler when the clock at that marking read t=13", any attempt to turn such local facts into statements about distances or velocities means you are making coordinate-dependent statements.Passionflower said:So you are claiming that ruler distance and radar distance as measured by a clock for static observers depend on the chosen coordinate chart in a Schwarzschild solution?
Why do you have to make things personal like this? I would have said the same if someone else was making your argument about coordinate-independence, and it's not like there haven't been plenty of times I've agreed with you about stuff. This is a discussion board, everyone's opinions get challenged periodically, no need to make bitter remarks about it and create bad feelings for no good reason.Passionflower said:Anything goes to 'prove' me wrong I suppose.
I apologize JesseM.JesseM said:Why do you have to make things personal like this? I would have said the same if someone else was making your argument about coordinate-independence, and it's not like there haven't been plenty of times I've agreed with you about stuff. This is a discussion board, everyone's opinions get challenged periodically, no need to make bitter remarks about it and create bad feelings for no good reason.
So just one posting before you posted this I showed a graph plotting the ruler distances between two observers divided by the radar time as measured by a clock at the observer closest to the EH for different distance. Clearly you can see that light takes more time for pairs closer to the EH. But you simply seem to re-raise the same question as if this posting never happened? Am I wrong in this?PAllen said:The seemingly open question here is whether there is a physically meaningful, preferred, way to talk about a non-local measurement of lightspeed in the radial direction by a (non-inertial) static observer at some fixed position above the event horizon. If there is well defined answer to this, it would not surprise me that this comes out different from c.
Good points, so I showed my work here: https://www.physicsforums.com/showpost.php?p=2980825&postcount=17.pervect said:Well - if you've done the calculation, you should be able to answer Pallen's questions, of how you define simultaneity, and along what particular curve you integrate the distance.
Just coming up with an answer isn't very convicing, if you can't show your work and define what it is that you're calculating when asked for details.
I see the plot but don't know it's meaning because I haven't seen definitions of key terms like ruler distance.Passionflower said:So just one posting before you posted this I showed a graph plotting the ruler distance between two observers divided by the radar time as measured by a clock at the observer closest to the EH for different distance. Clearly you can see that light takes more time for pairs closer to the EH. But you raise the question as if this posting never happened.
Out of curiosity do you understand the plot and did you make any conclusions yourself? Or perhaps you disagree with the result, perhaps you think I miscalculated something? Or did you decide to simply ignore what I wrote?
Passionflower said:l
Good points, so I showed my work here: https://www.physicsforums.com/showpost.php?p=2980825&postcount=17.
Now since you asked for them it would be very polite to comment on them right?
So you think the calculations are they right or wrong?
The speed of light in a gravitational field is not a constant value and is affected by the strength of the gravitational field. In a vacuum, the speed of light is approximately 299,792,458 meters per second, but in a strong gravitational field, such as near a black hole, it can be significantly slower.
Gravity affects the speed of light by warping the fabric of space-time. This warping causes the path of light to bend, making it appear to travel slower in a strong gravitational field. Additionally, the gravitational field can also affect the frequency and wavelength of light, further altering its speed.
The theory of general relativity, proposed by Albert Einstein, explains how gravity works as a result of the curvature of space-time. This theory also predicts that the speed of light will vary in different gravitational fields. This prediction has been confirmed through various experiments and observations.
According to the theory of relativity, nothing can travel faster than the speed of light. This holds true even in a gravitational field. While the speed of light may be slower in a strong gravitational field, it is still the maximum speed that any object can travel.
The speed of light in a gravitational field plays a crucial role in our understanding of the universe. It helps us to explain phenomena such as gravitational lensing, where the path of light is bent by a massive object, and the redshift of light from distant galaxies. It also plays a role in the study of black holes, which have extremely strong gravitational fields that can significantly affect the speed of light.