The Arrow of Time: The Laws of Physics and the Concept of Time Reversal

[Dale]

To say the laws of thermodynamics are not time-reverse symmetric is potentially a little misleading though

dS/dt > 0 is not time-reverse symmetric, no if's and's or but's. Thermodynamics may not be a "fundamental law", but its equations are clearly and unambiguously not time-reverse symmetric.

 

[PeterDonis]

dS/dt > 0 is not time-reverse symmetric, no if's and's or but's. Thermodynamics may not be a "fundamental law", but its equations are clearly and unambiguously not time-reverse symmetric.

Yes, but JesseM is correct that the *reason* we observe that law to hold is not any asymmetry in the fundamental laws. It's just that our past has a low-entropy boundary condition--the universe we live in started out in a very low entropy state--whereas our future does not.

As for *why* we impose that low-entropy boundary condition on our past, it looks like that has already been discussed in these forums--see https://www.physicsforums.com/showthread.php?t=48076".

 

[JesseM]

dS/dt > 0 is not time-reverse symmetric, no if's and's or but's. Thermodynamics may not be a "fundamental law", but its equations are clearly and unambiguously not time-reverse symmetric.

Are you talking about thermodynamics or statistical mechanics though? In statistical mechanics, if you pick a microstate randomly from a system's phase space and it happens to be a low-entropy one, then if you use the dynamical laws to project it forwards it's very likely to be in a higher-entropy state in the future, but it's equally true that if you use the dynamical laws to project it backwards and find the state at earlier times, it's very likely to have been in a higher entropy-state in the past too (and for a large system, very likely means overwhelmingly likely). So without any special choice of early boundary conditions, statistical mechanics is totally time-symmetric in this sense.

 

[Dale]

I am talking about thermodynamics. But the point remains that not all laws of physics are time reverse symmetric. Newtons laws are, as are GR and SR. Thermodynamics and the standard model are not. You can also do the same analysis for other laws of physics regardless of if they are a fundamental law, for example, Ohm's law is not time reverse symmetric, but Hooke's law is. You don't need to go to first principles, you can simply look at the equations and the quantities associated with each law and determine the symmetry.

 

[JesseM]

I am talking about thermodynamics. But the point remains that not all laws of physics are time reverse symmetric. Newtons laws are, as are GR and SR. Thermodynamics and the standard model are not. You can also do the same analysis for other laws of physics regardless of if they are a fundamental law, for example, Ohm's law is not time reverse symmetric, but Hooke's law is. You don't need to go to first principles, you can simply look at the equations and the quantities associated with each law and determine the symmetry.

Agreed, but I think it is a good thing to know that all fundamental laws are believed to be either T-symmetric or CPT-symmetric (and violations of T-symmetry in a CPT-symmetric theory like the Standard Model only crop up in certain esoteric areas of particle physics), so any time you have a non-fundamental law which is not time-symmetric, you can bet that the reason for it has to do with the fact that this approximate law is dealing with a situation where entropy is increasing, so that it's just a special case of the asymmetry in the second law of thermodynamics. For example, I couldn't tell you the exact connection between the asymmetry of Ohm's law and entropy increase, but I'm confident it must be there (something to do with resistors dissipating the energy of the current as heat, presumably).

 

[Dale]

Agreed, but I think it is a good thing to know that all fundamental laws are believed to be either T-symmetric or CPT-symmetric

I also agree.

I couldn't tell you the exact connection between the asymmetry of Ohm's law and entropy increase, but I'm confident it must be there (something to do with resistors dissipating the energy of the current as heat, presumably).

Yes, exactly. In a resistor energy always goes from low entropy electrical energy to high entropy thermal energy, never the reverse. But you can see the asymmetry directly from the Ohm's law equations without any knowledge of how those equations relate to entropy and thermodynamics.

 

[atyy]

Yet I have read interpretations of this as as being positively entropic.

Yes.
http://arxiv.org/abs/0812.2610
Statistical mechanics of gravitating systems: An Overview
T. Padmanabhan

What is the entropy of a black hole?

Yes, classical black holes are a problem for thermodynamics. Apparently quantum mechanics saves the day.
http://arxiv.org/abs/gr-qc/9702022
Black Holes and Thermodynamics
Robert M. Wald

 

[ernestpworrel]

I definitely remember reading something official that said the laws of physics don't distinguish between the past and the future.

I've read something similar. What this actually means is that the entropy of the microsystem increases in either direction. Take the case of ice cubes. They start out as fully formed cubes with low entropy. They gradually melt into a pool of water which means the entropy has increased. However, there had to have been a pool of water in the first place for the ice cubes to form, which means evolution from a state of high entropy to one of lower entropy. You have high-entropy water becoming low-entropy ice becoming high-entropy water. So the water had higher entropy on both sides of the ice cube state. Of course, entropy is still conserved in the macrosystem.

The rest of your post had to do with time reversal. Physical laws allow time reversal in that they do not favor any particular direction in time, which is called time-reversal symmetry. Everyone else has done a good job explaining this.

 

[A-wal]

I read somewhere that an observer moving towards a black hole would never reach the event horizon until they reached the singularity. I thought it was here but maybe not. It stuck in my mind because I've never heard that before and it did kind of seem to make sense for the event horizon to be relative and not a fixed radius. Is that not right then? What about for an observer moving quickly past the black hole? Surly length contraction would mean that the event horizon moves inwards as you approach it and move into a stronger gravitational field? Isn't it the equivalent of how you can go faster than light from the perspective of the distance in your original frame? So you can escape the event horizon using it's radius from another frame but that frame will see you as outside the event horizon in the same way as your original frame won't see you moving faster than c?

I take it that's not right then? The event horizon is the same radius in all frames? That's not very relative.

 

[Austin0]

Austin0, everyone agrees that the laws of thermodynamics are not time-reverse symmetric. That is why everyone was so careful to say "Newtons laws" etc. above, in order to specify that we were only talking about laws of physics that are time-reverse symmetric.

The fact that thermodynamics is not time-reverse symmetric does not change the fact that a planet orbiting clockwise is every bit as valid a solution to Newtons laws as a planet orbiting counterclockwise and that one is the time-reverse of the other. You do not have to reverse the course of the entire universe in order to be able to clearly state that Newton's laws are time reverse symmetric.

HI Sorry if I went slightly off the general thrust of this thread.
I do have question in line with the concept.
As I understand Thermodynamics , including entropy, it itself does not propose any fundamental concepts but is a generalized, statistical description of the workings of other
physical principles and forces.
The conservation of mass and energy, the kinetic interactions of particles, intermolecular forces,[Van der Wall etc] and at extreme ranges various QM effects.
If ,at the fundamental level, all these individual interactions and forces are time-symetric, what principle would lead to the aggregate results not also being time-symetric.
More specifically ,friction, heat dissappation etc are simply intermolecular tranfers of kinetic energy correct??
Is it quantum uncertainty that makes this movie not run backwards equally well?
Thanks

 

[Dale]

If ,at the fundamental level, all these individual interactions and forces are time-symetric,

They are not all time-symmetric (T symmetry), they are charge-parity-time-symmetric (CPT symmetry). Although some people like to say that the T asymmetry (more commonly known as a CP violation) is minor, it nonetheless establishes a fundamental arrow of time.

what principle would lead to the aggregate results not also being time-symetric.

All of the laws of physics are incomplete descriptions. They require additional information, called boundary conditions, in order to describe a physical situation. Asymmetries can arise from the boundary conditions, even with symmetric laws. Thermodynamics essentially does a statistical analysis of all possible boundary conditions to make its asymmetric conclusions.

Is it quantum uncertainty that makes this movie not run backwards equally well?

It is uncertainty, but I would include general measurement uncertainty and incomplete descriptions of systems and not limit it to quantum uncertainty.

 

[JesseM]

I take it that's not right then? The event horizon is the same radius in all frames? That's not very relative.

The word "frames" is not very clear in general relativity--in the context of SR it's usually used to refer to the particular set of coordinate systems known as inertial frames, so a given inertial observer will have a unique "rest frame", but in GR there is no similar set of preferred global coordinate systems in curved spacetime, you are free to use pretty much any type of coordinate system imaginable (with arbitrary coordinate values for the radius of a physical object like a black hole) according to the principle of "diffeomorphism invariance", discussed a bit http://www.aei.mpg.de/einsteinOnline/en/spotlights/background_independence/index.html . If we want to speak in coordinate-independent terms, though, we can just talk about proper time along the worldline of an observer falling into a black hole, and all coordinate systems will agree in their prediction about the proper time when the event horizon is crossed, which is a finite value and is also prior to the proper time when the worldline ends at the singularity (also at a finite value of proper time).

 

[A-wal]

Yea my terminology is a bit off. I use the word frame to mean the strength of the gravitational field as well. But I was also asking about whether relative velocity to the black hole would effect the radius of the event horizon. The proper version of being in a different frame. So the radius is the same regardless of length contraction either from relative velocity or gravitational field strength? I know this hasn't got much to do with the original topic but I'm getting to that.

 

[JesseM]

Yea my terminology is a bit off. I use the word frame to mean the strength of the gravitational field as well.

What do you mean by "as well"? I didn't say anything about frame being used to represent strength of field, a "frame" always refers to some kind of spacetime coordinate system which allows you to assign position and time coordinates to any event.

But I was also asking about whether relative velocity to the black hole would effect the radius of the event horizon.

But the "radius" of anything can only be defined in terms of the coordinates of some spacetime coordinate system...for instance, if one end of an object is at x=10 meters in your coordinate system, and the other is at x=15 meters, then the object would be 5 meters long in this coordinate system. As I said, in GR you can use absolutely any coordinate system (did you look at the article on diffeomorphism invariance), and any object should be able to have any length under the right choice of coordinate systems. So if you want to ask meaningful questions about the length or radius of something, you first need to specify what type of coordinate system you want to use.

 

[A-wal]

Okay I think we're having a breakdown in communication here. I think of a different frame as a frame which is time dilated/length contracted relative to another frame, whether it be from a difference in relative velocity or from a difference in gravity.


Yes I read the article and it didn't tell me anything I didn't already know. In fact it didn't say anything that I hadn't figured out before I started checking out the official stances on these concepts, although there are some good links on that page.


I read or heard somewhere that the event horizon recedes when it's approached, which I'd never heard before and it got me thinking.

If the event horizon recedes then it could mean that nothing can cross the event horizon in any frame which makes sense. If your observing something approaching a black hole then you will never see it reach the horizon. How close have you got to be? Right along side it? If you can't cross the event horizon in any frame then it would mean that both in falling and outside observers see exactly the same thing but measure it differently because they're in different frames, meaning the event horizon and the singularity are the same thing basically. Time stops at the event horizon for external observers and at the singularity for falling observers right? How close do you have to be to be classed as falling in? It suggests to me that the event horizon can't be crossed in any coordinate system.

 

[FayeKane]

A-wal, can you give me a ref about the event horizon receding when it's approached?

I assume you mean "as seen by a guy in a spaceship approaching the hole".

Is that due to the gravitational redshift slowing time? If so, how could that be detected by the guy in the spaceship; time is only slowed when viewed from a different inertial frame, right?

--faye kane, idiot savant

 

[JesseM]

Okay I think we're having a breakdown in communication here. I think of a different frame as a frame which is time dilated/length contracted relative to another frame, whether it be from a difference in relative velocity or from a difference in gravity.

But what would it mean, precisely, for a "frame" to be time dilated or length contracted relative to another? Can you give a numerical example? In terms of inertial frames, I would say that a physical clock at rest in one frame, and which ticks at the same rate as coordinate time in that frame (i.e. between time coordinates t=0 and t=10 seconds, the clock has ticked forward by ten seconds as well), is said to be time dilated in other inertial frames since it ticks slower than coordinate time in these frames (i.e. between time coordinates t'=0 and t'=10 seconds in another frame, the clock might only have ticked forwards by 8 seconds). But this is a statement about physical clocks being time dilated, not about one frame being dilated relative to another (keep in mind that for inertial frames in SR, each frame sees clocks at rest in other frames to be dilated relative to their own coordinate time). And when people talk about gravitational time dilation in GR, typically they aren't talking about multiple frames at all, they're just talking about the ticking rate of clocks relative to coordinate time in a single coordinate system like Schwarzschild coordinates. In Schwarzschild coordinates around a black hole or other spherical mass, if you look at clocks hovering at different fixed values of the radial position coordinate, the ones at a closer radius will be ticking slower relative to coordinate time than the ones at a farther radius. Schwarzschild coordinates are designed to have the property that only in the limit as the radius approaches infinity will a clock tick at the same rate as coordinate time, and if a clock A at some finite radius sends light signals with each one of its ticks to a clock B "at infinity", then the ratio between the rate clock B ticks and the rate that it receives signals from clock A should be the same as the ratio between the rate that clock B ticks relative to coordinate time and the ratio between the rate that clock A ticks relative to coordinate time. So, the amount a clock is slowed down relative to coordinate time in Schwarzschild coordinates is the same as the visual rate it looks to be slowed down when viewed by a very distant observer (for clocks at constant radius).

Yes I read the article and it didn't tell me anything I didn't already know.

OK, so take note of the last animated diagram on that page, showing you can draw your spacetime coordinate grid in totally arbitrary ways (all those different distorted 'grids') and the laws of GR will still be the same in this coordinate system. Based on this, it should be obvious that you can put as many meter-increments between two ends of an object as you want, so the coordinate length of an object can be anything you want it to be.

I read or heard somewhere that the event horizon recedes when it's approached, which I'd never heard before and it got me thinking.

I can't really make sense of that. Without knowing where you read or heard this, it's hard to say what's going on--maybe the author was mistaken, or maybe you're misremembering or you misunderstood, or maybe the author was using a particular coordinate system where this is true, or talking about what is seen in the case of an object falling into an evaporating black hole as discussed in the "What about Hawking radiation?" section near the bottom of this page.

If the event horizon recedes then it could mean that nothing can cross the event horizon in any frame which makes sense.

Again, if you're not using "frame" to refer to a spacetime coordinate system then I have no idea what you mean by that word. In Schwarzschild coordinates it's true that an object takes an infinite coordinate time to reach the event horizon, but there are other common coordinate systems used for a nonrotating black hole where things cross it in finite coordinate time, like Eddington-Finkelstein coordinates or Kruskal-Szekeres coordinates (illustrated near the bottom of this page). Of course, all coordinates agree that an observer remaining outside the horizon will never see anything cross the horizon visually.

 

[Austin0]

For one thing you have to take into account that as a cloud of gas contracts under its own gravity, the potential energy of all the particles decreases and is converted into kinetic energy, which means that even though there is a smaller range of available position-states, there is a higher range of available momentum-states--and the "entropy" of a given macroscopic state is determined by the total number of precise microscopic states compatible with that macroscopic states, with each distinct microscopic state corresponding to a precise specification of each particle's position and momentum (although in quantum mechanics the precision is limited by the uncertainty principle).

It turns out, though, that the increase in available momentum states as a cloud contracts is not sufficient to explain how the contraction can represent an overall increase in entropy--John Baez discusses this in detail on this page. He gives a hint about the true answer here, I think I remember someone saying that a fair amount of the energy lost as the gas cloud collapses is converted into photons (or just electromagnetic waves if we're talking about classical physics), so that the entropy of the collapsed cloud plus the photons is higher than the entropy of the original diffuse cloud. If that's not what Baez meant by the hint, though, someone please correct me!

Thanks for that link. I didnt get new info but Baez is a very engaging writer and I plan to look at more.
I agree with everything you have said here including the photon conclusion buuuuut
Would you agree that the concept of potential is somewhat tricky.
It seems to fall out of the essential conservation laws as a sort of bookkeeping balance principle. Obviously useful . It would seem that it is then also conservative. If conservation validly applies to the universe as a whole then the potential was also set by intial conditions although it obviously varies locally.
It also seems like one functional definition of positive entropy is; the maximal actualization of potential?
As you pointed out, any local , exploitable area of negative entropy almost inevitably implies a previous state of positive entropy. And vice versa.
This would seem to suggest that entropy itself could possibly be a conservative concept, depending on the final conditions of the universe.
Taken into the realm of the gravitationally condensing cloud, if we interpret the reduction of gravitational potential as a positive flow, would this not mandate a reappraisal of the previously considered positive flow of kinetic dispersal .as now being an entropically negative increase in gravitational potential??
Following the positive condensation there is the E negative release of atomically generated EM energy into the system .some of which is then positively dispersed throughout freespace.
So it would appear that the generalized trend toward positive entropy resides in this increasing amount of dispersed photon energy and the mass conversion and reduced gravitational potential implicit in its production. And ultimately ,what happens from there.
In a periodic universe it is possible that through time, all this energy will be reabsorbed through local matter or black holes, with an increase of G potential and an eventual collapse or possibly white holes and what is the entropy of that situation??
Conversely, in a perpetually expanding universe it can be imagined that eventually all the fusion potential will be expended and the existent photons will all eventually be drawn into black holes that are still expanding , in which case that would seem to be ultimately positive entropy by any difinition.
ANy thoughts ?

 

[A-wal]

I can't really make sense of that. Without knowing where you read or heard this, it's hard to say what's going on--maybe the author was mistaken, or maybe you're misremembering or you misunderstood, or maybe the author was using a particular coordinate system where this is true, or talking about what is seen in the case of an object falling into an evaporating black hole as discussed in the "What about Hawking radiation?" section near the bottom of this page.

I don't know where I got this from. I think I read it somewhere but it might have just come from me. Maybe I did misread something. I'll put it another way. I'm at rest relative to a black hole (using energy to resist being pulled in) and I measure the radius as ten whatever units. I now use energy to accelerate towards it and measure its radius to be eight units from the event horizon to the singularity in a straight line from me because of length contraction in this different inertial frame. I've now reversed and am back where I started so the radius is again ten units. This time I just stop using energy and let myself drift towards it. Wont the event horizon recede inwards towards the singularity as I accelerate towards it, this time because of gravitational length contraction? If not, wtf not?

 

[JesseM]

I'll put it another way. I'm at rest relative to a black hole (using energy to resist being pulled in) and I measure the radius as ten whatever units.

In the context of what coordinate system? Schwarzschild coordinates? Do you remember my point about how any object can have any length depending on your choice of coordinate system, and in GR all coordinate systems are equally valid because of diffeomorphism invariance? Do you disagree with this point?

I now use energy to accelerate towards it and measure its radius to be eight units from the event horizon to the singularity in a straight line from me because of length contraction in this different inertial frame.

But as I've told you before, in curved spacetime there is no such thing as an "inertial frame" globally, they can only be defined in a local sense (a patch of spacetime small enough that the curvature is negligible on that patch). Any coordinate system large enough to contain the whole event horizon of a black hole would presumably be too large for the curvature to be negligible, so it could not be an inertial frame.

Wont the event horizon recede inwards towards the singularity as I accelerate towards it, this time because of gravitational length contraction? If not, wtf not?

What is "gravitational length contraction"? Do you have a source for this notion or did you invent it yourself by analogy with length contraction in inertial SR frames?

 

[BigFairy]

What we do have to learn about the universe are bodies in relative motion, with the motion of no body preferred to any other, and that is all we need to do physics.

 

[A-wal]

@FayeKane: Sorry mate, forgot about your question. I still don't know where I got it from. Perhaps I dreamt it. Yes I do mean as seen by a guy in a spaceship approaching the hole. No you wouldn't be able to feel time dilation. It's not a different inertial frame, that's relative velocity. I'm talking about length contraction though. Obviously you can't feel that either but you would notice it if you compared your length to external objects. A black hole for example.

I'll put it another way. I'm at rest relative to a black hole (using energy to resist being pulled in) and I measure the radius as ten whatever units.

In the context of what coordinate system? Schwarzschild coordinates? Do you remember my point about how any object can have any length depending on your choice of coordinate system, and in GR all coordinate systems are equally valid because of diffeomorphism invariance? Do you disagree with this point?

It doesn't matter! Use whatever coordinate system makes you happy. As long as we keep using that coordinate system, who gives a flying bleep? Who's Schwarzschild?

I now use energy to accelerate towards it and measure its radius to be eight units from the event horizon to the singularity in a straight line from me because of length contraction in this different inertial frame.

But as I've told you before, in curved spacetime there is no such thing as an "inertial frame" globally, they can only be defined in a local sense (a patch of spacetime small enough that the curvature is negligible on that patch). Any coordinate system large enough to contain the whole event horizon of a black hole would presumably be too large for the curvature to be negligible, so it could not be an inertial frame.

Okay, we're a very long way away from the black hole. It makes no difference. Are you deliberately trying to be as awkward as possible?

Wont the event horizon recede inwards towards the singularity as I accelerate towards it, this time because of gravitational length contraction? If not, wtf not?

What is "gravitational length contraction"? Do you have a source for this notion or did you invent it yourself by analogy with length contraction in inertial SR frames?

What? Is that a joke? How else do you explain gravitation? Length contraction in every direction outward using an inverse square law because that's the relationship of length in relation to the volume in three dimensions = GRAVITY! If the event horizon varies due to the time dilation of being in a different inertial frame then the same should apply to gravitation. If it does then the event horizon would always be in front of you. You could never cross it until you reach the singularity. I'm not saying I'm right. I'm saying I can't see where this is wrong.

 

[JesseM]

In the context of what coordinate system? Schwarzschild coordinates? Do you remember my point about how any object can have any length depending on your choice of coordinate system, and in GR all coordinate systems are equally valid because of diffeomorphism invariance? Do you disagree with this point?

It doesn't matter! Use whatever coordinate system makes you happy. As long as we keep using that coordinate system, who gives a flying bleep? Who's Schwarzschild?

Schwarzschild is the guy who came up with the GR solution we now call a "black hole", and the coordinate system he used to describe it is also the most common one for physicists to use when dealing with the region outside the event horizon. Anyway, if you agree that all length is coordinate-dependent, then questions like "how does the black hole's radius change as you approach it" must be coordinate-dependent too, right? There would be a coordinate system where it shrunk, another where it grew, and another where it stayed the same (this last one would be true of Schwarzschild coordinates by the way, the radius of a black hole is unchanging in these coordinates).

I now use energy to accelerate towards it and measure its radius to be eight units from the event horizon to the singularity in a straight line from me because of length contraction in this different inertial frame.

But as I've told you before, in curved spacetime there is no such thing as an "inertial frame" globally, they can only be defined in a local sense (a patch of spacetime small enough that the curvature is negligible on that patch). Any coordinate system large enough to contain the whole event horizon of a black hole would presumably be too large for the curvature to be negligible, so it could not be an inertial frame.

Okay, we're a very long way away from the black hole. It makes no difference. Are you deliberately trying to be as awkward as possible?

You aren't really making any sense. I'm not talking about where "you" are, I'm talking about the region of spacetime that your coordinate system is supposed to cover. If the coordinate system only covers a region that's "a very long way away from the black hole" so that spacetime is approximately flat in this region and the coordinate system can be considered inertial, well then, this coordinate system obviously can't be used to define the radius of the black hole if the region of spacetime it covers doesn't contain any black hole!

What? Is that a joke? How else do you explain gravitation? Length contraction in every direction outward using an inverse square law because that's the relationship of length in relation to the volume in three dimensions = GRAVITY!

Uh, according to who? I've never seen any scientist "explain" gravitation in this way in the context of GR, is this an idea you made up yourself or do you have some source for it? In GR, "gravitation" is normally explained in terms of mass and energy curving spacetime, and the way that gravity changes the motion of passing objects is explained in terms of objects following geodesic worldlines in curved spacetime.

If the event horizon varies due to the time dilation of being in a different inertial frame then the same should apply to gravitation.

What do you mean "the event horizon varies due to the time dilation of being in a different inertial frame"? You really need to explain your ideas or give a source that explains them, I have no idea what you're talking about here.

 

[A-wal]

Schwarzschild is the guy who came up with the GR solution we now call a "black hole", and the coordinate system he used to describe it is also the most common one for physicists to use when dealing with the region outside the event horizon. Anyway, if you agree that all length is coordinate-dependent, then questions like "how does the black hole's radius change as you approach it" must be coordinate-dependent too, right? There would be a coordinate system where it shrunk, another where it grew, and another where it stayed the same (this last one would be true of Schwarzschild coordinates by the way, the radius of a black hole is unchanging in these coordinates).

You've lost me here. Length is coordinate dependent but whether length increases or decreases is also coordinate dependent? If something gets longer or shorter, surely it does so regardless of the coordinate system used?

You aren't really making any sense. I'm not talking about where "you" are, I'm talking about the region of spacetime that your coordinate system is supposed to cover. If the coordinate system only covers a region that's "a very long way away from the black hole" so that spacetime is approximately flat in this region and the coordinate system can be considered inertial, well then, this coordinate system obviously can't be used to define the radius of the black hole if the region of spacetime it covers doesn't contain any black hole!

I didn't think that inertial length contraction had a range. If I were to move directly towards something at a very high relative speed then length contraction would shorten the distance no matter how far away the object was. So we can be far enough away from the black hole to ignore the effects of its gravity and consider ourselves to be completely inertial yes? Besides, you make it sound as though the effects described in special relativity just disappear in a gravitational field above a certain strength.

Uh, according to who? I've never seen any scientist "explain" gravitation in this way in the context of GR, is this an idea you made up yourself or do you have some source for it? In GR, "gravitation" is normally explained in terms of mass and energy curving spacetime, and the way that gravity changes the motion of passing objects is explained in terms of objects following geodesic worldlines in curved spacetime.

Same thing!

 

[JesseM]

You've lost me here. Length is coordinate dependent but whether length increases or decreases is also coordinate dependent? If something gets longer or shorter, surely it does so regardless of the coordinate system used?

No, because we are dealing with spacetime coordinate systems of a totally arbitrary nature, and the notion of "changing length" just means the difference in coordinate positions between two ends of an object at different coordinate times. For example, regardless of what the object is or what is physically happening to it, there's nothing stopping me from designing my coordinate system so that at t=0 seconds, the back end is at x=0 meters and the front is at x=100 meters, but then at t=2 seconds, the back end is at x=0 meters and the front is at x=100000 meters (likewise, there's nothing stopping me from picking a coordinate system where at t=2 seconds the back is at x=0 meters and the front is at x=0.000000000001 meters). Again, just look at the last animated diagram on http://www.aei.mpg.de/einsteinOnline/en/spotlights/background_independence/index.html to get a sense of what it means to allow totally arbitrary distorted coordinate systems (and feel free to imagine that the y coordinate in this animated diagram is really a time coordinate and that the shapes represent different events in spacetime).

I didn't think that inertial length contraction had a range. If I were to move directly towards something at a very high relative speed then length contraction would shorten the distance no matter how far away the object was.

It's only meaningful to talk about length contraction of an object if you have a coordinate system that actually covers the object itself and can be used to assign position coordinates to each end of the object at different time coordinates. If your coordinate system just covers a small patch of spacetime, then in the context of that coordinate system it is meaningless to talk about the "length" of objects that are outside of that patch of spacetime. So if you want to talk about how the length of the black hole is changing you need a coordinate system covering a region of spacetime that actually includes the black hole, and this coordinate system will necessarily be a non-inertial one because the curvature of spacetime won't be negligible over the entire region.

Besides, you make it sound as though the effects described in special relativity just disappear in a gravitational field above a certain strength.

Even in special relativity "length contraction" only makes sense in the context of inertial frames, you can perfectly well pick a non-inertial coordinate system where a particular object's length expands as it gains velocity, or oscillates, etc.

What? Is that a joke? How else do you explain gravitation? Length contraction in every direction outward using an inverse square law because that's the relationship of length in relation to the volume in three dimensions = GRAVITY!

Uh, according to who? I've never seen any scientist "explain" gravitation in this way in the context of GR, is this an idea you made up yourself or do you have some source for it? In GR, "gravitation" is normally explained in terms of mass and energy curving spacetime, and the way that gravity changes the motion of passing objects is explained in terms of objects following geodesic worldlines in curved spacetime.

Same thing!

Care to explain? Your thought processes may be obvious to you but they aren't to me, and I doubt anyone else reading this thread understands what you mean either. How does explaining gravity in terms like "mass curves spacetime, and objects follow geodesic paths in curved spacetime" have anything to do with explaining gravity in terms of "length contraction"? And again, can you tell me if this is some idea you came up with on your own or whether you have a source for it?

 

[Dale]

If something gets longer or shorter, surely it does so regardless of the coordinate system used?

I have not been following the conversation very closely but it seems to me that you are talking about a measured length while JesseM is talking about a coordinate length. The results of measurements are indeed coordinate independent. Perhaps you could describe how you would measure the length of a black hole using a stationary measuring apparatus and a moving measuring apparatus.

 

[JesseM]

I have not been following the conversation very closely but it seems to me that you are talking about a measured length while JesseM is talking about a coordinate length. The results of measurements are indeed coordinate independent. Perhaps you could describe how you would measure the length of a black hole using a stationary measuring apparatus and a moving measuring apparatus.

But in a curved spacetime, since rigid rulers are impossible there are an infinite variety of different measurement procedures you could use, no? And for each coordinate system where objects at constant position coordinate have a timelike worldline, wouldn't there be a corresponding physical measurement procedure involving a network of measuring devices that were at rest in those coordinates, such that they would always give the same answer for lengths as the coordinate system itself? In this case there doesn't seem to be a lot of distinction between the notion of coordinate length and the notion of measured length.

 

[Dale]

But in a curved spacetime, since rigid rulers are impossible there are an infinite variety of different measurement procedures you could use, no?

Yes. That is why it would be important for A-wal to be explicit about the specific measurement procedure.

And for each coordinate system where objects at constant position coordinate have a timelike worldline, wouldn't there be a corresponding physical measurement procedure involving a network of measuring devices that were at rest in those coordinates, such that they would always give the same answer for lengths as the coordinate system itself?

I am not really sure one way or the other, but in any case his question (as I understand it) isn't if the number you get would match some coordinate system, it is if you would get a different result using a measuring procedure at rest wrt the black hole or moving wrt it. Of course, it is probably best if I let him speak for himself.

 

[A-wal]

If I measure the distance to the black hole to be 101 light years and the distance from the event horizon to the singularity is .001 light year and I accelerate to a speed where the distance to the black hole is now 10 light years (it took 1 light (in the original frame) to accelerate), what would I measure the event horizon to be? If it were a star instead of a black hole then the edge of the star would extend outward relative to the contracting space-time, but a black hole event horizon is space-time. It should contract inward. Or to put it another simpler way; what would the shape of the event horizon of a black hole look like if it was flying past us at very nearly c?

If the effect of gravity at the event horizon is equivalent to a relative verlocity of c, what would happen to the distance between the event horizon and the singularity as you approach it?

 

[JesseM]

If I measure the distance to the black hole to be 101 light years and the distance from the event horizon to the singularity is .001 light year

Measure it how? Using what coordinate system, or what physical measurement procedure? There is no single "natural" way to do measurements over large distances in curved spacetime because you can't have rigid measuring-rods in curved spacetime (and measuring distance also requires a simultaneity convention, since the idea is to measure the distance from one end to the other at a single moment in time).

There seems to be this presupposition in all your questions and arguments that "distance" and "measurement" have some unique well-defined meaning for a given observer in GR. They don't, so you need to understand that and either drop this line of argument or reframe it in terms of some particular procedure for defining "distance" out of the infinite variety of equally valid options that can be used in GR.

 

[ryuunoseika]

I definitely remember reading something official that said the laws of physics don't distinguish between the past and the future. I thinkit might have been A Brief HistoryOf Time. You could run it backwards and it would still work just as well. But now I've thought about it, there's something I can't resolve. Take two objects in space that are static relative to each other. They would gravitate towards each other. Now if time was running backwards then they would be moving away from each other. So gravity would be a repulsive force. But that doesn't work because if time was running backwards on Earth, we would still be pulled towards the planet, not pushed away. In other words it would work in freefall/at rest, but not when accelerating against gravity. How can it be both repulsive and attractive at the same distances?

Think about the ultimate final result of the two gravitating particles: they would ultimately collide and, provided that they are perfectly ellastic, bounce back to their original starting potential then fall again. They would repeat this pattern forever, and thus, at any point in time they could be reversed and it would look exactly the same, the only diffence is that, when viewed in a reversed arrow of time, a bounce is gravity pulling and gravity isa bounce.

 

[A-wal]

There seems to be this presupposition in all your questions and arguments that "distance" and "measurement" have some unique well-defined meaning for a given observer in GR. They don't, so you need to understand that and either drop this line of argument or reframe it in terms of some particular procedure for defining "distance" out of the infinite variety of equally valid options that can be used in GR.

I'm getting on your nerves now aren't I? Sorry but I just don't see how it makes any difference when comparing a change in length. If something extends or contracts then surely it does so no matter how it's measured. I'm not trying to be a twat and I do appreciate the responses but I still get the impression that you know what I mean and you're just trying to be awkward.

I am not really sure one way or the other, but in any case his question (as I understand it) isn't if the number you get would match some coordinate system, it is if you would get a different result using a measuring procedure at rest wrt the black hole or moving wrt it. Of course, it is probably best if I let him speak for himself.

Yes, and what the effect of gravity itself would be at the event horizon given that it's the equivalent to moving at c.

If I measure the distance to the black hole to be 101 light years and the distance from the event horizon to the singularity is .001 light year and I accelerate to a speed where the distance to the black hole is now 10 light years (it took 1 light (in the original frame) to accelerate), what would I measure the event horizon to be? If it were a star instead of a black hole then the edge of the star would extend outward relative to the contracting space-time, but a black hole event horizon is space-time. It should contract inward. Or to put it another simpler way; what would the shape of the event horizon of a black hole look like if it was flying past us at very nearly c?

I messed that up! It was late and I was in a hurry. I should have said 100 as the starting distance and then reverse 1 ly and then get a run up to cross the same point (marked by a nearby clump of matter before JesseyM says "What do you mean the same point?") at full speed. I was trying to avoid instant acceleration because you can't be moving if you haven't gone anywhere.

 

[Dale]

Sorry but I just don't see how it makes any difference when comparing a change in length.

It does make a difference. It is a question of definition. What do you mean by "length" of a black hole?

Yes, and what the effect of gravity itself would be at the event horizon given that it's the equivalent to moving at c.

That is not correct. There was a thread about this recently, and here was my comment in that thread:

If you have a very large black hole, such that the tidal forces at the event horizon are approximately zero, then that is equivalent to a Rindler accelerating observer in flat spacetime. Not an inertial observer at any speed.

 

[A-wal]

It does make a difference. It is a question of definition. What do you mean by "length" of a black hole?

I understand that if something is undefinable then it's meaningless. And I get that you can use any coordinate system for measurement. I still don't see the problem. If something is at rest (using energy to stay at a constant distance) relative to a black hole then the event horizon has a definite radius, yes? If the object then stops using energy to resist gravity then it will move towards the black hole, yes? Now, you could change coordinate system and say that you've moved away from the black hole. It's technically true and completely beside the point. Whether or not a black holes event horizon changes as you approach it is just as valid a question as whether you move towards or away from something exerting a gravitational force, yes? As long as keep using the same coordinate system, the question makes sense, yes?

That is not correct. There was a thread about this recently, and here was my comment in that thread:If you have a very large black hole, such that the tidal forces at the event horizon are approximately zero, then that is equivalent to a Rindler accelerating observer in flat spacetime. Not an inertial observer at any speed.

Are you saying that it's not equivalent to moving at c but only with black holes above a certain size? That doesn't seem right. If it's variable then it would only be equivalent to c if the black hole just happened to be exactly the right size, but that's not what I've heard/read (from multiple sources).

 

[Nabeshin]

Are you saying that it's not equivalent to moving at c but only with black holes above a certain size? That doesn't seem right. If it's variable then it would only be equivalent to c if the black hole just happened to be exactly the right size, but that's not what I've heard/read (from multiple sources).

Technically it holds for any size black holes, you simply need to make measurements over a much shorter time/distance interval so that the equivalence principle still holds. The point of making it a large black hole is that time scales are on the order of what is manageable to make measurements (seconds, minutes, etc.). Besides, there are no observers moving at c. So to talk about anything equivalent to that is meaningless in the first place.

The point is, an observer freely falling past the event horizon notices nothing special.