Length contraction of falling things

[jartsa]

1: Does an observer, standing on the moon, see a brick, that is falling straight down, to contract?

2: Does an observer, standing on the moon, see a light pulse, that is falling straight down, to contract?

 

[GAsahi]

1: Does an observer, standing on the moon, see a brick, that is falling straight down, to contract?

Yes.

2: Does an observer, standing on the moon, see a light pulse, that is falling straight down, to contract?

The answer to this question is much more complicated, the detailed mathematical explanation can be found here, I just posted it a few days ago.

 

[jartsa]

The answer to this question is much more complicated, the detailed mathematical explanation can be found here, I just posted it a few days ago.

Oh yes, the contraction is proportional to blue shift. And the simplest blue shift case is very simple.

Here's something people here may disagree with:

The contraction happens because the font of the light pulse moves slower than the rear of the light pulse. And that happens because light slows down in a gravity field.

 

[GAsahi]

Oh yes, the contraction is proportional to blue shift. And the simplest blue shift case is very simple.

I don't know where you get this but it is wrong.

Here's something people here may disagree with:

The contraction happens because the font of the light pulse moves slower than the rear of the light pulse.

You are making up stuff.

 

[jartsa]

I don't know where you get this but it is wrong.

Well, from here: https://www.physicsforums.com/showpost.php?p=3957856&postcount=15

 

[GAsahi]

Well, from here: https://www.physicsforums.com/showpost.php?p=3957856&postcount=15

You obviously cannot follow the math. Nor do you understand the physics.

 

[pervect]

1: Does an observer, standing on the moon, see a brick, that is falling straight down, to contract?

2: Does an observer, standing on the moon, see a light pulse, that is falling straight down, to contract?

What's your motivation for asking the question?

If you're trying to understand SR better, dragging GR into it isn't really a good way to proceed. You're much better off handling the simpler case in flat space-time where there's no gravity to confuse the issue.

If you're trying to understand GR better, it would be a good idea to sketch exactly how you propose to measure the length of the object remotely. I can warn you in advance that the notion of "distance" in general relativity is ambiguous, mainly due to differing notions of simultaneity. Some people understand the warning, some don't, and I get a bit frustrated trying to explain the problem to those who don't. This is really a SR issue, by the way, but it's an important one to understand before you try to tackle GR.

I can tell you how in general I would go about "setting up" the problem. The first step is to decide what notion of simultaneity you want to use, and why. So I would start by assuming that the moon is the most significant gravitating body, and that we can ignore the Earth. Right away, I can see a possible conflict with your question, perhaps you didn't intend the moon to be the most significant gravitating body? In that case, the issue of how to determine the notion of simultaneity would require some thought. If the moon is the most significant source of gravity, however, there is an obvious way to proceed, that is to use a clock synchronization scheme compatible with "static observers". It's less obvious how to proceed if the moon is not the most significant source of gravity.

Once you have decided on the notion of simultaneity you're going to use, the simplest procedure is to construct a spatial geodesic curve. (Not a space-time geodesic, but a spatial geodesic!). Constructing this geodesic will require you to use the metric induced on your spatial hypersurface by your space-time geometry. Constructing the geodesic will require some knowledge of the geodesic equations, and how to solve them. Solving them directly is usually difficult, and taking advantage of conserved quantities via means of Killing Vectors or some equivalent procedure, is highly recommended.

Next you need to confirm that the problem that you've set up is really one-dimensional. If it is, then you mark on this spatial geodesic curve the position of the front end of the rod, and another mark for the rear end of the rod, "at the same time", according to your notion of simultaneity. If both ends of the object aren't on a single curve, then your problem isn't one dimensional. But let's assume that it is. Then the length along the curve (the spatial geodesic) between the marks on the front and rear will be the "length of the rod".

I'm afraid I can't give an exact formula for the result you'd get if you followed this procedure, I'd actually have to work it. My own view is that the exercise of thinking about what you want to measure is considerably more helpful than going through the detailed calculations of calculating the number. Furthermore, if you don't understand what all the steps I've outlined mean (and some of them might require a certain amount of expertise), just giving you the number won't really accomplish much.

 

[jartsa]

What's your motivation for asking the question?

I could use some new facts in my thought experiment building hobby.

Let's say the light pulse is catched into a box which is just large enough. This is done at many different altitudes, with many light pulses.

Then all boxes are moved into same place and compared.

I would guess the boxes from lower altitudes are smaller, and light in these boxes has more energy.

 

[pervect]

I could use some new facts in my thought experiment building hobby.

Let's say the light pulse is catched into a box which is just large enough. This is done at many different altitudes, with many light pulses.

Then all boxes are moved into same place and compared.

I would guess the boxes from lower altitudes are smaller, and light in these boxes has more energy.

If you raise or lower a meter stick, oriented normally to the gravitational force so the change in stress doesn't cause the length to vary, I can't see any reason for it to change it's length.

So I would say that the same applies to a box, say a microwave cavity filled with one wavelength of microwave radiation. The local physics will be the same, the cavity/box won't change length, and a local frequency counter would measure the same frequency, the constant length of the cavity divided by c, no matter what the height of the box was.

The energy-at-infinity would change as you raised the box, but I think this could eventually be traced back to the work done in raising the radiation in the box. It will take more work to raise a box full of microwave radiation than one that's empty. I'm not aware of ay formal p roof of the matter, but I don't see how it could be otherwise.

 

[harrylin]

[..] Here's something people here may disagree with:

The contraction happens because the font of the light pulse moves slower than the rear of the light pulse. And that happens because light slows down in a gravity field.

People can disagree with anything - and often it very much depends on definitions of words.
But it's a simple fact that if according to a distant observer a stationary meter rod is length contracted and a clock at one end is ticking slower, that then with that reference system the return speed of light can only be measured as c if the light according to the distant observer is slowed down with gamma squared (using a standard and consistent meaning of words).

PS: As Shapiro's phrased it, "the speed of a light wave depends on the strength of the gravitational potential along its path" - http://prl.aps.org/pdf/PRL/v13/i26/p789_1 .
See also discussions on "Shapiro time delay" and note that according to GR the rod will not be contracted if held parallel to the surface.

 

[Dale]

light slows down in a gravity field.

Similarly to your misconception about clocks slowing down, in GR light (in vacuum) also does not ever slow down in a coordinate independent sense. It always travels along null geodesics.

Even in flat spacetime, it is possible to write down coordinates in which the coordinate speed of light is faster or slower than c, but these are obviously coordinate-dependent statements. Anywhere in any spacetime that you find a set of coordinates where light slows down there are also other sets of coordinates where it does not.

 

[Q-reeus]

I could use some new facts in my thought experiment building hobby.

Let's say the light pulse is catched into a box which is just large enough. This is done at many different altitudes, with many light pulses.

Then all boxes are moved into same place and compared.

I would guess the boxes from lower altitudes are smaller, and light in these boxes has more energy.

Agree entirely with that observation. And it agrees I believe with what #10 was intending to convey. One just needs to be careful in defining precisely the relative nature of 'length change' in such situations.

 

[Q-reeus]

If you raise or lower a meter stick, oriented normally to the gravitational force so the change in stress doesn't cause the length to vary, I can't see any reason for it to change it's length.

In SC's transverse length in coordinate measure expressly is invariant wrt potential, but not if that rod is radially oriented (and that's with 'stress' subtracted out). But 'radially shortened' is imo only of value in the sense that integrating over an extended radial path r2 to r1 (coordinate measured), there is more proper distance covered in the interval r2-r1 than if gravity were switched off. We all agree that locally no length or time distortions can logically be evident.

So I would say that the same applies to a box, say a microwave cavity filled with one wavelength of microwave radiation. The local physics will be the same, the cavity/box won't change length, and a local frequency counter would measure the same frequency, the constant length of the cavity divided by c, no matter what the height of the box was.

Which is distinctly different to OP's scenario - free-falling light pulse measured at different heights by a 'hovering ruler' (the box in effect).

The energy-at-infinity would change as you raised the box, but I think this could eventually be traced back to the work done in raising the radiation in the box. It will take more work to raise a box full of microwave radiation than one that's empty. I'm not aware of ay formal p roof of the matter, but I don't see how it could be otherwise.

Sure, and that gets back to arguments I was making elsewhere re 'charged BH' and elsewhere - EM field energy associated with charges/currents of a non-free-fall system, is depressed in a gravitational potential by redshift factor. Not so for geodesic propagating light beam.

 

[harrylin]

Agree entirely with that observation. And it agrees I believe with what #10 was intending to convey. One just needs to be careful in defining precisely the relative nature of 'length change' in such situations.

Size yes, but energy I don't know - that's a tricky topic. My guess would be that the total energy doesn't change.

 

[HallsofIvy]

I could use some new facts in my thought experiment building hobby.

Let's say the light pulse is catched into a box which is just large enough. This is done at many different altitudes, with many light pulses.

Then all boxes are moved into same place and compared.

I would guess the boxes from lower altitudes are smaller, and light in these boxes has more energy.

Even in "thought" experiments, you cannot just ignore basic facts of physics. You cannot "catch" light in a box and move it.

 

[harrylin]

Even in "thought" experiments, you cannot just ignore basic facts of physics. You cannot "catch" light in a box and move it.

Doesn't that come close to "Einstein's box" ?
- http://en.wikipedia.org/wiki/Bohr–Einstein_debates

 

[jartsa]

Similarly to your misconception about clocks slowing down, in GR light (in vacuum) also does not ever slow down in a coordinate independent sense. It always travels along null geodesics.

Even in flat spacetime, it is possible to write down coordinates in which the coordinate speed of light is faster or slower than c, but these are obviously coordinate-dependent statements. Anywhere in any spacetime that you find a set of coordinates where light slows down there are also other sets of coordinates where it does not.

Well, then I guess I must be saying things in a coordinate dependent sense. Is that a bad thing?

 

[jartsa]

Size yes, but energy I don't know - that's a tricky topic. My guess would be that the total energy doesn't change.

Well of cource it changes. Light that falls, and bounces back, does not change. Light that falls, and is lifted back, does change.

 

[Dale]

Well, then I guess I must be saying things in a coordinate dependent sense. Is that a bad thing?

No, it isn't a bad thing as long as you understand what you are doing and are clear about it. Otherwise it leads to confusion, which I believe is reflected in your writing.

 

[Dale]

Well of cource it changes. Light that falls, and bounces back, does not change. Light that falls, and is lifted back, does change.

My guess would be the same as harrylin's. I don't think that the "of course" is warranted, unless you have a completely foolproof derivation in three lines or less.

 

[pervect]

Well, then I guess I must be saying things in a coordinate dependent sense. Is that a bad thing?

It is possible to say things correctly in a coordinate dependent manner, just difficult. For instance, you need for starters to specify what coordinates what you're saying is valid in. This usually leads to rather long explanations. Coordinate independent explanations don't need all the background, so they can usually be much shorter.

So, if you don't like writing a lot, and in great detail, it's a big advantage to talk in coordinate independent terms. It's also easier (for the most part) for the reader to follow.

Of course, it's also possible to say things in a coordinate dependent manner that are just plain wrong. (It's possible to say wrong things in a coordinate independent manner too, of course).

I'll use an example I've used before of saying something that's just plain wrong. Suppose you're talking about length contraction, in the context of the surface of the Earth, and you start saying that "distances are smaller near the poles". Hopefully, it's obvious that this is just plain wrong.

But let's examine what you might be thinking, a related concept that isn't wrong.

Now, you might be thinking in a coordinate dependent manner, and what you are really trying to say is that one arc second of longitude near the equator is longer than one arc second of longitude near the poles. This would be correct, unlike saying that "distances are shorter near the poles".

The fundamental mistake that was made here is conflating (confusing and combining) differences in coordinates, i.e. changes in lattitude, and distances. The two concepts are different. The first concept is not a distance. You can, however convert it to a distance by using the local metric coefficients. After you've performed the appropriate connection, it becomes a distance.

I often see the same type of error made in relativity, in relation to the Schwarzschild R coordinate. Conceptually, it's a coordinate, not a distance. It doesn't become a distance until you apply the metric to it.

 

[harrylin]

Well, then I guess I must be saying things in a coordinate dependent sense. Is that a bad thing?

It isn't really coordinate dependent, however it's "reference frame" dependent. And while some people seem to think that that's a bad thing, others don't. For example, many physicists don't think that it's a bad thing to talk about "high energy" electrons. Of course, in such cases the reference is clearly implied.

Well of cource it changes. Light that falls, and bounces back, does not change. Light that falls, and is lifted back, does change.

A material object "falls" by accelerating towards the gravitating body, and in that process we can imagine that potential energy is transformed into kinetic energy. I think that the total energy of such a two body system in isolation must remain constant, as determined with a non-local reference inertial system. In contrast, and as you suggested yourself, light that propagates directly towards the gravitating body does not accelerate towards it but decelerates; moreover it looks to me that it has only kinetic energy which should remain constant from that perspective as long as the box is not moved (I could be wrong there, but for sure its frequency is unchanged). Next, moving the box demands more analysis.
So, in view of those points, please elaborate your thought experiment - which, it seems, has little to do with your topic.

 

[jartsa]

It isn't really coordinate dependent, however it's "reference frame" dependent. And while some people seem to think that that's a bad thing, others don't. For example, many physicists don't think that it's a bad thing to talk about "high energy" electrons. Of course, in such cases the reference is clearly implied.

A material object "falls" by accelerating towards the gravitating body, and in that process we can imagine that potential energy is transformed into kinetic energy. I think that the total energy of such a two body system in isolation must remain constant, as determined with a non-local reference inertial system. In contrast, and as you suggested yourself, light that propagates directly towards the gravitating body does not accelerate towards it but decelerates; moreover it looks to me that it has only kinetic energy which should remain constant from that perspective as long as the box is not moved (I could be wrong there, but for sure its frequency is unchanged). Next, moving the box demands more analysis.
So, in view of those points, please elaborate your thought experiment - which, it seems, has little to do with your topic.

We can drop light into a box, lift the box, take light out, move box back down, drop the light into the box, lift the box ... energy is used, it must go somewhere, the light is the only alternative.

UNLESS light is weightless. If light is weightless form of energy, we can very easily build a perpetual motion machine. So it's not weightless.

Let's define weight as exchange of momentum with a gravitating object. We probably agree that light bends in a gravity field, and momentum change happens when light bends.

What happens to light that moves straight up or straight down ... that's an interesting question.

 

[Naty1]

I could use some new facts in my thought experiment building hobby.

I think you mean some basic facts from which to draw conclusions and make thought experiments?

A few to get started:

[1] All local clocks [of good quality] tick at the same rate. A clock here and a clock there tick at the same rate, but neither may appear to do so to a DISTANT observer. Another way to say this is that clocks record proper time, and that is not dependent on the coordinates used, nor the path you take. Any clock you carry with you records your local age and local processes along your worldline...your path through space and time. In GR, clocks don't slow down in any coordinate-independent sense; they measure proper time along their worldline, your worldline if you are carrying the clock, which is an invariant quantity. [2] The local speed of light is always c. This means light always travels at the same speed 'c' right where you are. The speed of light as observed in curved spacetime varies, that's general relativity, but right where you are [locally] spacetime is flat and light is always observed at speed 'c'. This seems somewhat 'crazy' at first because no matter your speed relative to anything else, light still zips by you at the constant 'c'. That idea takes a while to get used to.
In special relativity, meaning flat spacetime, all inertial observers see light at speed 'c'. This means distant and local observers. But for accelerating observers, things change... observations vary.

 

[Naty1]

Jartsa:

We can drop light into a box, lift the box, take light out, move box back down, drop the light into the box, lift the box ... energy is used, it must go somewhere, the light is the only alternative.

UNLESS light is weightless. If light is weightless form of energy, we can very easily build a perpetual motion machine. So it's not weightless. Let's define weight as exchange of momentum with a gravitating object. We probably agree that light bends in a gravity field, and momentum change happens when light bends. What happens to light that moves straight up or straight down ... that's an interesting question.

WHOAAA! You have way too much stuff going on...ambiguous terminology...too many conflicting ideas with erroneous statements and conclusions...slow down, dude! seems like ideas pop into your head and you write them down...instead, take ONE idea and give it some thought as to the consequences of what you are posting ...

First off; light has no mass...but you cannot willy nilly draw conclusions from that such as 'no mass [no weight] so no work' with your box questions ...and 'no mass' does NOT mean because it is 'weightless' you can build a perpetual motion machine...that's mostly gibberish. [Energy is equivalent to mass via E =mc² and light has energy; this means it is gravitationally attractive like everything else we know.]

So before we talk about light in boxes going up and down let's look at a few basics:

[These have been fully discussed elsewhere in these forums, so if I can remember them, they'll be correct and maybe we can even find all the detailed discussions if required]Let's say a bunch of observers have identical light sources...all have the same reference color [frequency]. A series of local observers at different gravitational potentials, say at fixed distances in a uniform gravitational field, would each subsequently observe a photon passing their own location to have different red shift [different energy, different color] relative to a local reference photon. Each measures velocity 'c'. [from my post above]
This means the kinetic energy of observed photons has changed...such KE increases as gravitational potential decreases. Light further down becomes blue shifted.

[Different coordinate perspective: From the viewpoint of a free falling observer at rest in the freely falling frame, there is no "gravitational field". She is weightless, feeling no force, so to her, local physics looks the same as in free space with no gravity. Photons in free space with no gravity do not redshift. So the motion of the observer is critical to what KE they measure.]Another example: Suppose a flashlight shines down into a deep gravitational well with a lead shield at the bottom: could it penetrate the lead shield?

Answer is yes: The light picks up kinetic energy [is blueshifted] and loses potential energy as it falls: that means a flashlight beam becomes like gammas rays [lots more KE if the gravitational potential is strong enough]. So in theory it can punch thru the shield.

I think this is also accurate: Another view: If you move a lead shield rapidly enough against a flashlight beam, the beam can also in theory punch through that shield: the shield 'sees' the light as extremely energetic...really short frequency...these views are equivalent...Ok: so what do you conclude will be the characteristic of such light 'boxed' by different observers. Right where they make the observation. Then maybe we can figure what happens when the light is removed outof the gravity well??

 

[harrylin]

J[..]
So before we talk about light in boxes going up and down let's look at a few basics:

[These have been fully discussed elsewhere in these forums, so if I can remember them, they'll be correct and maybe we can even find all the detailed discussions if required]

[..] The light picks up kinetic energy [is blueshifted] and loses potential energy as it falls: that means a flashlight beam becomes like gammas rays [lots more KE if the gravitational potential is strong enough]. [..]

Hmm I also remember them, and according to me the consensus in the scientific literature is contrary to what you say - and I also disagree with your conclusions.
According to you, if you change your perspective, is it then accurate to say that kinetic energy "changes"? I think that that is misleading. Moreover, according to GR reference clocks at lower gravitational potential tick slower (that is, as observed with a stationary non-local reference system). Einstein predicted the redshift effect based on that conclusion. Your blueshift would be double the predicted and verified amount if you were right. In other words, your presentation denies gravitational time dilation. If you like, I can dig up a good physics paper about that (I think it was by Okun).

 

[jartsa]

I think this is also accurate: Another view: If you move a lead shield rapidly enough against a flashlight beam, the beam can also in theory punch through that shield: the shield 'sees' the light as extremely energetic...really short frequency...these views are equivalent...


Ok: so what do you conclude will be the characteristic of such light 'boxed' by different observers. Right where they make the observation. Then maybe we can figure what happens when the light is removed outof the gravity well??

Same characteristic. Light does not change when catched into a box.

 

[Dale]

Light does not change when catched into a box.

Sure it does, it either becomes a standing wave or becomes absorbed. It is no longer a wave in vacuum, but is interacting with matter. The equations that govern light's behavior change substantially. Have you ever done any actual EM?

 

[Dale]

jartsa, I agree strongly with Naty1's comments of post 25. You make such a slew of errors, strange assumptions, confused reasoning, and unsubstantiated assertions that it is hard to even know where to help you. You are just "all over the map", please slow down. Which one topic are you most interested in:

1) length contraction in gravity
2) speed of light in GR
3) coordinate dependence/independence
4) light in a box
5) something else ...

 

[Austin0]

Originally Posted by Naty1

J[..]
So before we talk about light in boxes going up and down let's look at a few basics:

[These have been fully discussed elsewhere in these forums, so if I can remember them, they'll be correct and maybe we can even find all the detailed discussions if required]

[..] The light picks up kinetic energy [is blueshifted] and loses potential energy as it falls: that means a flashlight beam becomes like gammas rays [lots more KE if the gravitational potential is strong enough]. [..]

Hmm I also remember them, and according to me the consensus in the scientific literature is contrary to what you say - and I also disagree with your conclusions.
According to you, if you change your perspective, is it then accurate to say that kinetic energy "changes"? I think that that is misleading. Moreover, according to GR reference clocks at lower gravitational potential tick slower (that is, as observed with a stationary non-local reference system). Einstein predicted the redshift effect based on that conclusion. Your blueshift would be double the predicted and verified amount if you were right. In other words, your presentation denies gravitational time dilation. If you like, I can dig up a good physics paper about that (I think it was by Okun).

In one view the difference in observed frequency is purely due to the dilation differential between the electrons of emission and reception.The photon retains its initial frequency throughout . There is no change in the photon during transit.

The other view is that the photon does change in transit. Gaining momentum into the well and comparably loosing it going uphill.

. Gravitational time dilation itself, is now a fact. SO this explanation totally accounts for the results. I.e. A difference in resonant frequencies of emitting and absorbing electrons due to dilation.
so the assumption of any additional factor at work would seem to necessitate additional observed end results above the gamma factor or be rejected.

There is no need for all sorts of mental gymnastics or contorted logic here. It is just a simple and clear experimental result (that light's energy is affected by gravity just like everything else's energy) and the usual understanding that energy is frame variant.

Coincidentally this same question came up in another recent thread where I expressed this same view as yourself, but it is seemingly not generally accepted by those here. ;-)

 

[harrylin]

[..] According to you, if you change your perspective, is it then accurate to say that kinetic energy "changes"? I think that that is misleading. Moreover, according to GR reference clocks at lower gravitational potential tick slower (that is, as observed with a stationary non-local reference system). Einstein predicted the redshift effect based on that conclusion. Your blueshift would be double the predicted and verified amount if you were right. In other words, your presentation denies gravitational time dilation. If you like, I can dig up a good physics paper about that (I think it was by Okun).

I now found it all back, we discussed it here in detail:

https://www.physicsforums.com/showthread.php?p=3166721
It also has a link to an earlier discussion of the topic by others.

And here's the abstract of Okun's paper:

The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in two ways: On the one hand, the phenomenon is explained through the behavior of clocks which run faster the higher they are located in the potential, whereas the energy and frequency of the propagating photon do not change with height. The light thus appears to be redshifted relative to the frequency of the clock. On the other hand, the phenomenon is alternatively discussed ͑even in some authoritative texts͒ in terms of an energy loss of a photon as it overcomes the gravitational attraction of the massive body. This second approach operates with notions such as the ‘‘gravitational mass’’ or the ‘‘potential energy’’ of a photon and we assert that it is misleading. We do not claim to present any original ideas or to give a comprehensive review of the subject, our goal being essentially a pedagogical one. - Okun AJP 2000

 

[harrylin]

Originally Posted by Austin0
" [..] Gravitational time dilation itself, is now a fact. SO this explanation totally accounts for the results. I.e. [..] the assumption of any additional factor at work would seem to necessitate additional observed end results above the gamma factor or be rejected.[..]"

OK, you explained the same as I did when I wrote: "blueshift would be double the predicted and verified amount if [light wave frequency increasing in transit] were right. In other words, [that] presentation denies gravitational time dilation." BTW, I forgot to mention that Einstein concluded the existence of gravitational time dilation in 1911 because the concept of an increasing number of cycles in transit is incompatible with wave theory.

But then you write (and I reinsert from your original quote + add detail for clarity, as the disagreement is about the way in which light's energy is affected by gravity!):

[..] ['in stationary frames (relative to the gravitating source) the energy [of radiation] increases as it goes down.] 'light's energy is affected by gravity' [...]
in another recent thread [..] I expressed this same view [..] but it is seemingly not generally accepted by those here.

Do you mean that according to you, as measured with a single inertial reference system, the energy of a photon in transit changes with the gravitational potential even though its frequency is not?

 

[harrylin]

We can drop light into a box, lift the box, take light out, move box back down, drop the light into the box, lift the box ... energy is used, it must go somewhere, the light is the only alternative.[..]

[..]Light does not change when catched into a box.

As others also remarked, that's just not good enough for physics discussions.
In order to make a valid argument that leads to a serious conclusion, you need to quantify your assertions based on laws of physics. If you do that, those lines may need to be expanded to fill perhaps half a page with equations or very good explanations that play the same role, and only then can we judge your proof and comment on it. That's what I meant with "more analysis". Now it's just a kind of hand waving.

 

[vin300]

" ['in stationary frames (relative to the gravitating source) the energy [of radiation] increases as it goes down.] 'light's energy is affected by gravity' [...] "
There had been discussions on this in a recent thread, about the energy of light increasing as it goes down. I always thought that the energy of an object falling or rising in a gravitational field doesn't change. The conclusion from that thread was that the energy of the photon doesn't change, but its frequency depends only on its kinetic energy, which I doubt. It helps to think about the equivalence principle here. The gravitational field is equivalent to an accelerating frame, and an accelerating observer obviously sees the light to be doppler shifted(change of energy). But since the field and the accelerating frame are equivalent and there is no change in photon energy in the field(from the earlier reasoning), DrGreg concluded that there's a pseudo-gravitational field associated with an accelerating frame, so that in this frame the energy of the photon is left unchanged. Honestly, now I don't know what to believe.

 

[Q-reeus]

jartsa: "We can drop light into a box, lift the box, take light out, move box back down, drop the light into the box, lift the box ... energy is used, it must go somewhere, the light is the only alternative.[..]"

jartsa: "[..]Light does not change when catched into a box."

As others also remarked, that's just not good enough for physics discussions.
In order to make a valid argument that leads to a serious conclusion, you need to quantify your assertions based on laws of physics. If you do that, those lines may need to be expanded to fill perhaps half a page with equations or very good explanations that play the same role, and only then can we judge your proof and comment on it. That's what I meant with "more analysis". Now it's just a kind of hand waving.

Maybe not as precisely presented as some demand, but taken in context the intention of jartsa's points above are more than reasonable, even logically necessary. The first is simply saying conservation of energy requires 'trapped light' to act gravitationally just as for rest matter. Cyclic process of hoisting+free-fall should be a zero-sum game. And that requires no locally observed frequency change when lifting the box (=perfectly reflective cavity resonator). Which is also the second point. One might argue hoisting process could somehow convert between the trapped EM field energy and overall box PE, but how?

Say for a cubical cavity resonator, resolve cavity field into three mutually orthogonal sets of counterpropagating traveling waves. Two sets propagating transverse to radial direction, one along that axis. Sets need not be equal amplitude. It should be obvious the two transverse sets have no appreciable coupling to the only conceivable factor that hauling-up process could bring to bear as locally measured - a changing gravity/tidal gravity. In the radial set case, it is equally obvious whatever is conceivably gained/lost by a traveling wave component in one direction is reversed during the other half trip. Perhaps for an exceedingly rapid 'snatch' process a tiny disequilibrium would occur, but up to critics to prove that matters here imo. And incidentally this kind of thing can be extended to say a box full of hot gas or whatever - there is no reason to suppose any such form of trapped energy acts differently to a dead lump of rest mass. Assuming varying gravity/tidal gravity is all there is to consider. And yet...

There is a possible caveat, stemming from my own earlier considerations in a thread dealing with angular momentum of a flywheel lowered into a potential well. We had assumed the flywheel's own angular momentum was invariant wrt potential, a reasonable assumption in keeping with conservation of angular momentum. Yet from a Machian pov that seems suspect. Time dilation demands that the coordinate determined spin-rate declines with lowering potential, and this in turn naively implies an increased coordinate flywheel mass to compensate. Problem is that would conflict with the two assumptions that rest mass/energy declines with lower potential and that EP holds true (inertial mass = active gravitational mass = passive gravitational mass). A redefinition of angular momentum in gravity well is thus necessary to at all reconcile these factors.
There is however an additional possibility - that angular momentum becomes progressively redistributed between flywheel proper and the rest of the gravitating mass system. Which is in keeping with the Machian position that inertia is a mutual effect between all mass/energy. Thus build a shell of mass around a flywheel and it's coordinate spin-rate declines, but one must expect an action of flywheel's motion back on the shell. And that seems at least roughly in line with a strictly GR 'frame dragging'. One might then conclude a varying gravitational and/or gravitational tidal force is not the only possible influence on 'light in a box'.

So yes I'm having it a bit both ways here!

 

[PeterDonis]

" ['in stationary frames (relative to the gravitating source) the energy [of radiation] increases as it goes down.] 'light's energy is affected by gravity' [...] "
There had been discussions on this in a recent thread, about the energy of light increasing as it goes down. I always thought that the energy of an object falling or rising in a gravitational field doesn't change.

It depends on how you define "energy" and how you define "change". Different people have different definitions they like, and they often will say (as the Okun paper that harrylin mentioned does--btw, harrylin, do you have a link to the paper itself?) that other definitions besides theirs are "misleadinng" or some such. The key thing IMHO is to remember that in GR, "energy" is not a fundamental concept; it's a way of interpreting the physics, but you don't need it to actually calculate what happens. You can calculate everything using covariant geometric objects like vectors and tensors, which have unambiguous definitions and behave in well-defined, unambiguous ways.

For example, take the photon free-falling radially towards a gravitating body. It has a 4-momentum vector p^{a} which is parallel transported along its worldline. Since parallel transport is one common way in GR of defining what it means for a geometric object to "not change" along a curve, this implies that the photon's 4-momentum does not change. And since the norm of the 4-momentum can be defined as the "energy at infinity" of the photon, some people interpret this as saying that the energy of the photon does not change.

However, the energy that the photon will be *observed* to have depends on the 4-velocity of the observer, via the equation:

E_{obs} = g_{ab} p^{a} u^{b}

Even if we interpret what I said above as p^{a} not changing as the photon falls, g_{ab} u^{b} *will* change, in general, for different observers. In particular, it will change for static observers at different altitudes, who will therefore observe the photon to have different energies, and therefore different frequencies, i.e., gravitational redshift/blueshift. Some people interpret this as saying that the energy of the photon *does* change.

Which interpretation is "right"? Does it matter? It depends on what you are using the interpretation for. Both interpretations agree on the actual physical observables, so as far as physics is concerned, they're equivalent. One may lead to more understanding and less confusion for some people, in some situations. But IMHO that's not a question of physics.

 

[vin300]

And since the norm of the 4-momentum can be defined as the "energy at infinity" of the photon, some people interpret this as saying that the energy of the photon does not change.

Isn't the norm of photon 4-momentum zero?

 

[PeterDonis]

Isn't the norm of photon 4-momentum zero?

Oops, yes, you're right, I was confusing the photon case with the timelike particle case. I should have just said that some people interpret the photon 4-momentum being parallel transported as its energy not changing.

 

[harrylin]

[..] btw, harrylin, do you have a link to the paper itself?

I gave a link to the paper itself
Perhaps you meant a link to a freely downloadable (=pirated) version, but no I don't have that. On the other hand, a personal message can have good results (hint).

[..] In particular, it will change for static observers at different altitudes, who will therefore observe the photon to have different energies, and therefore different frequencies, [..]

This issue may indeed be a matter of language. If you change your reference system from for example the ECI frame to the rest frame of a rocket to the moon, does that also change the distance Earth-moon? I will say no, your change of perspective cannot affect a distance. But some people might say yes to that question.

Both interpretations agree on the actual physical observables

Only if it's just a matter of formulation, and not if it's a case of truly disagreeing interpretation (it may be the one for some, and the other for some others!). Gravitational time dilation is observable independent of redshift; see posts #26 and #32.

 

[PeterDonis]

This issue may indeed be a matter of language.

I think in large part it often is. For example:

If you change your reference system from for example the ECI frame to the rest frame of a rocket to the moon, does that also change the distance Earth-moon? I will say no, your change of perspective cannot affect a distance. But some people might say yes to that question.

That's because the two of you are using the word "distance Earth-Moon" to refer to two different invariants; they are the invariant lengths of two different spacelike curves between the Earth's worldline and the Moon's worldline. Changing your perspective doesn't change either invariant, but it may change which one you think should be called "the distance Earth-Moon". But that's a question of terminology, not physics. When I said everyone agrees on all actual observables, I meant everyone agrees on the values of all invariants. They may disagree on what to call them.

 

[Austin0]

OK, you explained the same as I did when I wrote: "blueshift would be double the predicted and verified amount if [light wave frequency increasing in transit] were right. In other words, [that] presentation denies gravitational time dilation." BTW, I forgot to mention that Einstein concluded the existence of gravitational time dilation in 1911 because the concept of an increasing number of cycles in transit is incompatible with wave theory.

But then you write (and I reinsert from your original quote + add detail for clarity, as the disagreement is about the way in which light's energy is affected by gravity!):

Do you mean that according to you, as measured with a single inertial reference system, the energy of a photon in transit changes with the gravitational potential even though its frequency is not?

No,,,,my interpretation is the same as yours.You are confusing the quote of DaleSpams I inserted with my thoughts. The bolded above is his interpretation along with his assessment of my logic in reaching my conclusion.

 

[Austin0]

There is a possible caveat, stemming from my own earlier considerations in a thread dealing with angular momentum of a flywheel lowered into a potential well. We had assumed the flywheel's own angular momentum was invariant wrt potential, a reasonable assumption in keeping with conservation of angular momentum. Yet from a Machian pov that seems suspect. Time dilation demands that the coordinate determined spin-rate declines with lowering potential, and this in turn naively implies an increased coordinate flywheel mass to compensate. Problem is that would conflict with the two assumptions that rest mass/energy declines with lower potential and that EP holds true (inertial mass = active gravitational mass = passive gravitational mass). A redefinition of angular momentum in gravity well is thus necessary to at all reconcile these factors.
There is however an additional possibility - that angular momentum becomes progressively redistributed between flywheel proper and the rest of the gravitating mass system. Which is in keeping with the Machian position that inertia is a mutual effect between all mass/energy. Thus build a shell of mass around a flywheel and it's coordinate spin-rate declines, but one must expect an action of flywheel's motion back on the shell.

The spin rate declines according to which observer? The local or the observer at the initial elevation?

Could you elaborate on the assumption that "rest mass/energy declines with lower potential " ?

 

[harrylin]

I think in large part it often is. For example: [..].

It's good to see that you agree with my example. What is still not clear to me, if some people here actually have been misled by such language or not. You seem to think that this was clear for everyone - but I doubt that. Let's hope that it's at least now clear for everyone.

Perhaps it's better to give a crystal clear example:

Put an atomic clock in a high tower and synchronise¹ it with the ECI frame, as is commonly done. Tune a crystal oscillator to exactly 1.000 GHz with that atomic clock as reference, and use it for a radio emitter. There is a similarly tuned atomic clock and a radio receiver with frequency analyser on the ground. Send during exactly 24h a 1.000 GHz radio signal to the ground, 500 m below. According to GR the received signal as read on the frequency analyser will be exactly 1.000 GHz and the emission time exactly 24 h (in an ideal² situation). That should be clear and obvious to everyone.

Harald

ADDENDUM, notes:
1. tune it to run in sync, as is commonly done for time keeping
2. also overlooking that the ECI frame isn't perfectly inertial

 

[Naty1]

PeterDonis:

Since parallel transport is one common way in GR of defining what it means for a geometric object to "not change" along a curve, this implies that the photon's 4-momentum does not change. And since the norm of the 4-momentum [it is zero] can be defined as the "energy at infinity" of the photon, some people interpret this as saying that the energy of the photon does not change.

Peter: It was this issue that caused me to in my earlier post try to get the original poster back to basics first. He did not seem interested in that approach. I am still unsure what he wanted to accomplish by 'putting photons in a box'. Maybe he thought they would stay the same color forever if left in place? who knows.

In any case, I had been thinking that slowly raising photons from varying gravitational potential depths would result in a different characteristic of light at the surface versus them following null geodesics as when freely emitted; that some changes in characteristics would result. Can you comment about what you think happens?

 

[harrylin]

Maybe not as precisely presented as some demand, but taken in context the intention of jartsa's points above are more than reasonable, even logically necessary. The first is simply saying conservation of energy requires 'trapped light' to act gravitationally just as for rest matter. Cyclic process of hoisting+free-fall should be a zero-sum game. And that requires no locally observed frequency change when lifting the box (=perfectly reflective cavity resonator).

Apparently you assume that no light ray reflects off the bottom or the top during motion. That's not likely IMHO. And thus its effect should be analysed. Is then work done or not? And equal but opposite?

[..] the trapped EM field energy [..]

I would say trapped radiation energy - not field energy!

Say for a cubical cavity resonator, resolve cavity field into three mutually orthogonal sets of counterpropagating traveling waves. Two sets propagating transverse to radial direction, one along that axis. Sets need not be equal amplitude. It should be obvious the two transverse sets have no appreciable coupling to the only conceivable factor that hauling-up process could bring to bear as locally measured [..]

As discussed in parallel, analyses with "local" measurements easily complicates analysis. It can be useful to develop a theory but when you already have the theory, needless frame jumping is often counter productive.

[..] from a Machian pov that seems suspect. [..]

I find Machian POV's themselves suspect.
And I think that we have largely covered the topic of this thread.

 

[Dale]

According to GR the received signal as read on the frequency analyser will be exactly 1.000 GHz and the emission time exactly 24 h (in an ideal situation). That should be clear and obvious to everyone.

That is incorrect, and this contradicts both the Pound Rebka experiment and also current experiments done with atomic clocks at different heights.

 

[Dale]

Coincidentally this same question came up in another recent thread where I expressed this same view as yourself, but it is seemingly not generally accepted by those here. ;-)

I cannot tell from this comment nor from your follow-up comments whether or not you have any disagreement or any confusion from my quote.

 

[jartsa]

So here's what happens in the box that contains light and is being lifted:


Let us examine light in a mirror lined box, which is being lifted at a constant coordinate speed. The coordinate speeds of the ceiling mirror and the floor mirror are the same. The coordinate speeds of the light near the ceiling and the light near the floor are different.

Now we must study Doppler shift. When an EM-wave pulse and a mirror collide, the mirror receives wave crests at average frequency:
the number of crests in the wave / time that the collision lasts

Now, in the Doppler shift effect there is no change of number of wave crests in a wave pulse, so the change of the duration of the collision between the wave and the mirror is the thing that determines the Doppler shift.

An observer who is staying at constant altitude, and observing our box being lifted, says that near the ceiling the light has a larger coordinate speed, and therefore the duration of the collision between the ceiling mirror and the light is determined by the motion of the light in a greater degree as compared to the collision between the light and the floor mirror, so near the floor mirror the duration of the light-mirror collision is determined by the coordinate speed of the mirror in a greater degree, as compared to the situation near the ceiling.

So this observer at constant altitude says that light blue shifts, when being reflected from the floor mirror, more than it red shifts when reflected from the ceiling mirror, and therefore the observer observes a frequency increase of the light.

 

[Dale]

So this observer at constant altitude says that light blue shifts, when being reflected from the floor mirror, more than it red shifts when reflected from the ceiling mirror, and therefore the observer observes a frequency increase of the light.

Can you quantify that?

 

[PeterDonis]

Put an atomic clock in a high tower and synchronise it with the ECI frame, as is commonly done. Tune a crystal oscillator to exactly 1.000 GHz with that atomic clock as reference, and use it for a radio emitter. There is a similarly tuned atomic clock and a radio receiver with frequency analyser on the ground. Send during exactly 24h a 1.000 GHz radio signal to the ground, 500 m below. According to GR the received signal as read on the frequency analyser will be exactly 1.000 GHz and the emission time exactly 24 h (in an ideal situation). That should be clear and obvious to everyone.

As DaleSpam's comment on this post shows, it still isn't.

First of all, when you say "synchronise it with the ECI frame", I assume you mean not just adopting the standard of simultaneity of the ECI frame, but also its clock rate, correct? In other words, you are artificially setting the frequency of *both* oscillators, at different heights, to different clock rates than they would normally run at, similar to what is done with the clocks on board the GPS satellites. Only if you do this does your prediction of unchanged "frequency" with height make sense.

But of course this "frequency" that you are saying does not change with height is really a "coordinate frequency", not a "proper frequency"; it's not the "natural" frequency that at least one of the oscillators (and probably both) would measure if you hadn't artificially set them to the ECI clock rate. In other words, you are artifically tuning each oscillator so that the "frequency" that it measures is *not* the "natural" frequency that would be measured by an observer with the same 4-velocity. The "effective" 4-velocity of the oscillator for purposes of measuring frequency, what you would contract with the 4-momentum of the photon to compute its observed frequency, is some *other* 4-vector, a 4-vector that is associated with "coordinate time" in the ECI frame.

All of which illustrates that it's tough to be clear, even when you are really trying to be.