You’ve gone back to misunderstanding the equivalence principle. I doubt you’ll find any takers for resuming the discussion.
As has been pointed out no few times, you’re mis-stating the experiment.
Stop the second train, and let the man inside the train be pulled forward, against the forward wall of the cabin he is in. He cannot tell the difference between that and being thrown forward against the forward wall by a sudden emergency braking of the train. In both cases, he is accelerated with respect to his frame of reference, and there is no intrinsic difference between the effects of the two.
(This is the usual “elevator” model, just stood on one side.)
(Some persnickety types note that there are two differences: gravitational acceleration varies in strength from the front of the coach to the back of the coach, as the distance from the gravitationally attracting mass differs. Also, in practice, gravity tends to be toward a point, so the angle of the attraction would vary from the floor of the coach to the ceiling of the coach. Real physicists ignore this as irrelevant, or, more formally, “piddling.”)
To quote Gomez Addams, “I am that fool!”
If you were Inside a train car (a very very long one) that was in a vacuum and being accelerated at 1G by a gravitational field in front of it, then fired a bullet, the bullet would undergo its own chemical acceleration as expected, and gravity would keep pulling on the bullet at 1G + the acceleration introduced by the gunfire until it would outpace the train car.
Do this same experiment, in zero G, but the train car is being dragged through space by a rocket propelled engine undergoing continuous acceleration at 1G. You fire the gun, and the bullet will gain the chemical acceleration + the momentum it had the moment it left the gun barrel.
Compare the two bullets, and you should find that the “gravity bullet” will be accelerating ever faster than the “inertial bullet”. The “gravity bullet” will overtake its train, while the “inertial bullet” will be overtaken by its train.
But this isn’t a break in Relativity. It’s because the “gravity bullet” is still undergoing acceleration, because gravity is pulling on all the matter in the field homogenously.
Where as the the “inertial bullet” has been essentially removed from the engine/acceleration chassis, since there’s no air, it’s not being dragged like the gun and train still are, so the train will eventually overtake the bullet.
It’s late, but I think I got that right.
Which is, of course, exactly what the equivalence principle says, which is thus supported by the thought experiment. The mistake Hans then makes is to assume that objects distinct from the train should experience the train’s acceleration – this is forgetting the local nature of the equivalence principle. An equivalent to Hans’ thought experiment would be to have an observer standing outside of the train. In the case where the train falls towards a gravitational source, that outside observer would experience the same acceleration as the train; however, in the case of the train being accelerated by its engine, an outside observer would remain stationary. But the fact that a train can zip past you standing on the platform without you noticing much doesn’t disprove the equivalence principle, because there is no acceleration acting on you, similar to there being no acceleration acting on the bullet.
The acceleration imparted by the gravitational field acts uniformly on all objects, but the acceleration imparted by the train’s engine doesn’t. This is not a conflict with the equivalence principle, because it only holds for what the train’s engine imparts acceleration on, which, as you note, leads it (i.e. the train) to experience a situation locally indistinguishable from being in a gravitational field. In order to equalize both situations, you would have to imagine the observer on the train, the bullet, the laser, everything else experiencing their own acceleration – say, tying a rocket engine to all of them. Then, if such a thing were possible, everything on the train would have the same experience – weightlessness – as it would have if the train fell towards a gravitating mass, because everything would experience the same acceleration locally. If you break that condition, then you create a situation in which the equivalence principle doesn’t apply; that it then doesn’t hold is no great mystery.
Picture the acceleration imparted by a gravitating mass as a field distributed in space: at every given point, anywhere throughout space, it has a certain magnitude, so that an object placed there will experience a certain acceleration. In contrast, the train engine imparts its acceleration at only a single point, the front of the train (say)*. For that point, there is a local acceleration equivalent to a local acceleration in the gravitational field; only for that point, the equivalence principle is valid, and only there, it holds. Any other point in space will not experience the acceleration from the train’s engine – not a person on the platform, not a passenger on the train, not a bullet fired by the passenger. The mistake is in thinking that the equivalence principle would require the acceleration to act uniformly (‘uniformly’ here merely meaning ‘being present at every point’, not ‘being of the same magnitude everywhere’) throughout space; but this is of course a global property, and the equivalence principle is only about local properties.
*Of course, the acceleration can be distributed, by static forces, throughout the train’s frame – one can imagine this as the engine accelerating the very front of the train, that front accelerating the part immediately behind it via the forces that join the two, that part again accelerating the part behind it etc., like beads on a string that is being pulled.
Perhaps a picture will help. The equivalence principle essentially says that the equality in panel 1) holds; Zweig says that the inequality in panel 2) disproves the EQ. But both situations are inequivalent; panel 1) is about the local acceleration experienced by x, while panel 2) is about the accelerations experienced by x and o, which is not a local quantity. That in 2), situations a) and b) are inequivalent does not impact the EQ at all – it only says that situations a) and b) in 1) have to be equivalent (wrt x’s experience), which they are.
You have proved my point very succinctly. There is a difference in behaviour between the two situations. The two bullets are behaving differently, despite Einstein saying that the effects of gravity and acceleration are indistinguishable from each other. Where I made my mistake earlier in thinking that the two train experiment was flawed, was in trying to equate it to Einstein’s men in chests experiment. The two experiments are different. Einstein has acceleration pulling in one direction, and gravity pulling in the opposite direction. Zweig has both acceleration and gravity pulling in the same direction. Perhaps it is Einstein’s experiment which is flawed. As you have stated above, it is easy to distinguish the two when they are both pulling in the same direction.
To recap, if I am being pulled forward by a gravitational source, I will feel no acceleration, and if I fire a gun forward, the bullet will continue at its muzzle velocity till it hits the front of the train.
On the other hand, if I am being pulled forward by a mechanical source, I will feel the acceleration (eg 1G), and if I fire a gun forward, the bullet’s velocity will decrease relative to that of the accelerating train as time passes.
Einstein says that no experiment can detect the difference.
On reading the various posts on this subject since I re-opened it by saying that Hans is right after all, I notice a few posts acknowledging that there is a difference in the two situations, but also saying that the equivalence principle is not broken. Here is one such :-
“The acceleration imparted by the gravitational field acts uniformly on all objects, but the acceleration imparted by the train’s engine doesn’t. This is not a conflict with the equivalence principle, because it only holds for what the train’s engine imparts acceleration on, which, as you note, leads it (i.e. the train) to experience a situation locally indistinguishable from being in a gravitational field.”
That statement is in conflict with itself. The first half says there is a detectable difference, the second half says there is not.
The general concensus then is that there is a detectable difference, but I am saying this is in conflict with Einstein’s statement that a difference cannot be detected, where you are not.
But one thing we all agree on is that a difference can be detected!
Er, no, that isn’t the consensus. The consensus is that you’re wrong. You are proposing experiments to which the equivalence principle doesn’t apply. You’re mistaking “free fall” for “acceleration.” I’m sure you’re having fun, but what you’re doing is rotten science.
You’re not only moving the goal posts…you’re accelerating them.
The thing is just that the equivalence principle says that something being accelerated has the same experience as something in a gravitational field. That something not being accelerated – i.e. the bullet – does have a different experience is not in conflict with this; in fact, it follows trivially. Beyond this, I’m afraid I can’t help.
Trinopus said “The concensus is that you’re wrong”. The concensus a few hundred years ago was that the Earth was the centre of the universe.
You all seem to like Einstein’s men in chests experiment, and take it as gospel. Let’s take another look at that. Here is another quote from chapter XIX of the oft quoted book :-
“Bodies which are moving under the sole inflence of a gravitational field receive an acceleration whicih does not in the least depend either on the material or the physical state of the body. For instance a piece of lead and a piece of wood fall in exactly the same manner in a gravitational field (in vacuo), when they start off from rest or with the same initial velocity.”
In chapter XX where we have shifted to a chest being accelerated by a hypothetical being :-
“…the acceleration of the body towards the floor of the chest is always of the same magnitude, whatever kind of body he may use for the experiment.”
He did not actually stipulate that the gravity/acceleration was 1G, but we can take that as a given.
First the chest on the Earth. The chest is 20m high, and suspended at ceiling height is a large mass. This mass is in fact a miniature black hole which is the same mass as the Earth. The means of its suspension is immaterial. When that mass is dropped, how long will it take to hit the floor?
The Earth’s gravity is 9.8m/s^2 . The black hole’s gravity is 9.8m/s^2 . The total acceleration is therefore 19.6m/s^2.
t = sqrt( 2 * d / g ) = sqrt( 40 / 19.6 ) = 1.4
The black hole hits the floor of the chest after 1.4 seconds.
Second the chest which is being accelerated by the hypothetical being. The chest is identical to the chest on the Earth. The black hole is released, and hits the floor of the chest after :-
t = sqrt( 40 / 9.8 ) = 2
The black hole hits the floor of the chest after 2 seconds.
Einstein’s statement in chapter XX is correct. The mass, when released, is simply left behind as the chest accelerates away, so will fall at 9.8m/s^2 .
Einstein’s statement in chapter XIX is wrong. The mass falls* at the combined acceleration of the two masses, which in the case of the black hole is 19.6m/s^2 . In the case of the wood or lead, the acceleration is so close to 9.8m/s^2 as to be indistinguishable from that figure.
This explains why the piece of wood and lead appear to fall in exactly the same manner. Their mass is so tiny compared to the mass of the Earth, that any difference in acceleration between the two simply cannot be measured. If a black hole falls faster than a piece of lead or wood, then so does a mass half of that of the black hole, or a quarter, or a tenth etc. In principle, if the man’s instruments are sensitive enough, he can tell whether he is in a gravitational field or being accelerated (by a hypothetical being).
- Actually they both “fall” towards their combined centre of mass, but the man in the chest would see the mass fall as described.
You are misunderstanding Einstein’s writings in a number of ways. In your example with the black hole, the “Bodies which are moving under the sole influence of a gravitational field” are moving in a gravitational field which is the combined gravitational field of two massive bodies. So this is one case where you are simply misunderstanding/misapplying his writing. In your scenario you are correct that “the black hole hits the floor of the chest after 1.4 seconds.” But you are incorrect to use “9.8m/s^2” in your second calculation. Einstein’s point in the references you quoted would be that since the “influence of the gravitational field” was 18.6m/s^2, then in your second example the hypothetical being must accelerate at 18.6m/s^2. There is no problem there. But there is another way in which you seem to be misunderstanding Einstein. In your second example with the hypothetical being Einstein meant one of two things. One would be that the hypothetical being held the chest fixed, and accelerated the objects inside it (in the same way that the rock beneath your feet holds you fixed while gravity tries to accelerate you downward). In this case you are misapplying example 1, in which you assume the chest is NOT held fixed, because you are allowing the earth (and thus the chest) to move toward the black hole. So you are internally contradicting yourself. The second thing that Einstein might means is that both the chest and the objects inside it are accelerated equally by the hypothetical being, and in this case you are again misapplying Einstein’s prescription by not applying the acceleration imposed by the hypothetical being on the chest/earth in addition to the black hole. Either way, your examples are confused and flawed.
Let me tell you how the equivalence principle is usually explained (and this is the understanding Einstein held). Put the “chest” out in space and let gravity act on it. The chest will experience “free fall”, and if you put a person inside it, give him a lab and all sorts of objects to play with, he will not be able to tell that anything is wrong. The reason is because the chest, the floor beneath his feet, and all of the objects in his lab, all fall at the same rate in the gravitational field. In other words, the situation is the same as if a hypothetical being were uniformly accelerating every single atom in the lab (including the chest itself) at the same rate. In both cases, the scientist inside would not be able to tell that he was accelerating. The technical proviso to the equivalence principle is that space must be locally flat. If it is highly warped like next to a black hole, you get “tidal forces”. Einstein of course was well aware of that. So it might not be a good idea to include black holes in your examples. But nonetheless your point is that some objects in the lab inside the chest have different densities, and so alter the gravitational field. Can the scientist detect this? Sure! But he still wouldn’t be able to tell that he is accelerating!! In your example, if he really had a black hole inside his lab with the mass of the earth, he would fall into it! He would notice that! But he still wouldn’t know that he was being accelerated while falling into a black hole inside his lab. From his perspective, there would be nothing out of the ordinary in his lab except the black hole that happened to be there!
Does that answer your questions?
I see. So because you can think of a consensus that was wrong, all consensuses are now by definition wrong?
99.999999999% of the time, the consensus is right. That’s why it becomes a consensus.
The consensus is that f=ma, the area of a circle is [pi]r^2, e=mc^2, and so on. There are literally thousands upon thousands of them. Do you doubt them all? We use them all every day.
The reverse call to authority (I know of a consensus that was wrong, therefore all consensuses are invalid) is nonsense. It really depresses me when I see people trot that old pony out.
Another standard example is the “artificial gravity” of a spinning space station. Something like Niven’s Ringworld, or the spaceship Discovery in 2001: A Space Odyssey. If you are inside a spinning ring, you can’t tell if you’re being held to the floor by gravity or by “centrifugal force.”
(I know some physics profs don’t like that term, but it is valid in a rotating frame of reference…)
Otherwise…are we going to say, “Poor Einstein, he was so stupid that he couldn’t tell the difference between sitting in a chair and falling down a mine-shaft?” C’mon: the guy had his little lapses, but nothing like that!
(And Newton was so stupid, he thought all objects moved in straight lines. Must never have driven a cart along a winding road! And Aristotle was so stupid, he thought trees were made of dirt! And…)
No it does not, and for a number of reasons. You are telling me that I am misunderstanding Einstein, but it is you who are misunderstanding him. Read his book chapters XIX and XX which I am quoting from. A miniature black hole is one of Einstein’s objects which can be “dropped”. The fact - and it is a fact, is that it will drop faster than a piece of lead in the same scenario. Of course if the hypothetical being pulls the chest at 19.6m/s^2, the lead will hit the floor after 1.4s, but then we do not have two identical starting points, so that argument is invalid.
The hypothetical being holding the chest fixed and accelerating the objects inside it is also flawed. Read his book. If I stipulated that the Earth had to be held still, the acceleration between it and the BH would still be 19.6m/s^2 . In the accelerated chest, the acceleration is not imposed on the BH for the simple reason that once it is released, it has no mechanical conection to the chest, and is simply left behind as the chest accelerates away.
My examples are not confused and flawed, but your objections are.
Your misunderstandings are so numerous that it is difficult to respond. So I will restrict myself to one thing at a time. The hypothetical being should not be pulling the chest only. It should be pulling the chest and all of its contents, including the black hole. Your statement that “the acceleration is not imposed on the BH…” is based on a basic misunderstanding of what the hypothetical being does. Otherwise Einstein is giving an example I am unaware of, and you should provide the quote where he makes it clear, as well as the entire context so we can help you understand what Einstein is saying.
Now you’re just being silly. As has been pointed out several times, the equivalence between the accelerated frame and the stationary frame in a gravitational field is only local equivalent. Make the chest big enough or your instruments sensitive enough, and you’ll find that the gravitational field isn’t uniform. Make a chest big enough to fit in something with a significant gravitational field of its own, and you’ll find that dropping it gives you an increased acceleration in a gravitational field and not in an accelerated reference frame, at least if you can make accurate measurements that aren’t completely messed up by the rapid change of acceleration as the black hole gets close to them.
You do realize you now have the tidal forces of the black hole to separate from your other measurements?
Again read his book which I have quoted from many tmes. Here is my sentence in full, which you reproduced only part of above :- “In the accelerated chest, the acceleration is not imposed on the BH for the simple reason that once it is released, it has no mechanical connection to the chest, and is simply left behind as the chest accelerates away.”
The salient point being “when released”
Here is a direct quote from the book, if you don’t have a copy, although if you care to go back through this forum, you will find many quotes from it.
Chapter XX. (Chest is accelerateed by the hypothetical being). “If he release a body which he previously had in his hand, the acceleration of the chest will no longer be transmitted to this body, and for this reason the body will approach the floor of the chest with an accelerated relative motion.”
My wording is slightly different that’s all.
Quote. Originally Posted by iamnotbatman
. . . Let me tell you how the equivalence principle is usually explained (and this is the understanding Einstein held). Put the “chest” out in space and let gravity act on it. The chest will experience “free fall”, and if you put a person inside it, give him a lab and all sorts of objects to play with, he will not be able to tell that anything is wrong. The reason is because the chest, the floor beneath his feet, and all of the objects in his lab, all fall at the same rate in the gravitational field. In other words, the situation is the same as if a hypothetical being were uniformly accelerating every single atom in the lab (including the chest itself) at the same rate. In both cases, the scientist inside would not be able to tell that he was accelerating. . . . Quote.
The point you are missing here is that gravity accelerates all objects equally, whereas the hypothetical being can only accelerate objects with a mechanical connection. “…IF a hypothetical being were uniformly accelerating every single atom in the lab…” That would be gravity, not mechanical acceleration. The being can only use acceleration, not gravity, so by inserting that caveat, you are implicitly acknowledging that there is a difference.
Yes, but the point is that the EQ is only supposed to hold for those things that are being accelerated. Refer back to my drawing: only for x, the EQ holds; for o, it does not apply (or rather, it does apply, in the form that a non-accelerated thing has the same experience as an object in no gravitational field). I’m really not sure what the problem is: anything that has an acceleration acting on it has an experience equivalently to being in a gravitational field. You say that something that doesn’t have an acceleration acting on it having an experience as if it weren’t in a gravitational field is in conflict with this statement, but of course, it directly follows from it!
If something is not being accelerated, it should not have an experience equivalent to being in a gravitational field. And exactly that’s the case with the bullet (et al.): it’s not being accelerated, and thus, moves as if it weren’t in a gravitational field.
I don’t have the book. You are going to have to provide the full context. Otherwise I can only guess at the argument Einstein is making.
One way of expressing the equivalence principle, is to compare, as I did in my previous post, a chest in free fall in a gravitational field, to a chest in which every atom of it and its contents are being mechanically accelerated. This may be impractical, but it is possible in a thought experiment; this mechanical acceleration would not be the same as gravity. Now, there are other ways of talking about the equivalence principle which Einstein may be using, but which are less suited for talking about black holes inside the chest (only because you have to very carefully account for complicating factors). For instance you can compare a chest in a gravitational field that is NOT in free fall. For instance the chest is sitting on the surface of the earth. But here you have to be very careful, because the earth is a dynamic object which itself can experience acceleration. In this thought experiment every atom of the chest is being acted on by Earth’s gravitational field, while an equal and opposite mechanical force is being applied only to the chest’s floor in order to keep it in place. We can compare this to a chest being accelerated by a mechanical force (by a hypothetical being) equal to the force required to keep the chest in place on the earth. Now suppose you put a little black hole in the chest. The earth will be attracted to the black hole, and will accelerate towards it at 9.8m/s^2, so indeed in the rest frame of the chest the black hole will fall towards the floor of the chest at 18.6m/s^2. But now what mechanical forces are acting on the chest? Is it still the same 9.8m/s^2 as it was before we added the black hole with a powerful gravitational field? No! In order to figure it out, we have to add up the forces. Both the top and bottom of the chest are acted on by the earth’s gravitational field in the “-” direction, while the bottom of the chest is acted on in the “+” direction by the black hole, and the top of the chest is acted on in the “-” direction. Adding it up, the bottom of the chest experiences a net force of m0m/s^2, while the top of the chest experiences a net force of m18.6m/s^2. If you do the full integration over the chest correctly, you will end up with an average gravitational force on the chest of m9.8m/s^2 in the direction of the earth. Now, the surface of the earth is moving at 9.8m/s^2 towards the black hole, which means that the mechanical force acting on the chest from the surface of the earth is equal to m18.6m/s^2. Therefore the correct mechanical analogy is for a hypothetical being to accelerate the chest at 18.6m/s^2 which is in perfect agreement with your observation that the black hole will accelerate at 18.6m/s^2 towards the floor of the chest in either scenario.
So, having gone through the argument, you see that in order to account for everything correctly is a bit difficult, and though I have not read Einstein’s argument, it would not surprise me if he glossed over the technical treatment. In general you are adding unnecessary complications by using something like a black hole in equivalence principle thought experiments, because you are adding another gravitational field that you need to account for in your analogy using an equivalence with mechanical acceleration. Furthermore you are adding a gravitational “source term” inside the chest. Doing this starts making simple reasonings usually given for the equivalence principle to break down. It still all works out, but it gets more complicated. Another reason why using a black hole is not a good idea is that the equivalence principle doesn’t hold for objects extended over non-locally flat areas of space (you get tidal forces, etc).
You’ve got some smart people here (some of whom are actual physicists cough cough) who are kindly trying to help you figure out where your misunderstanding is coming from. I counsel you to take advantage of the situation.
Einstein’s Relativity : the Special and General Theory is available at project Gutenberg. (Click the title.)
It matches tomh4040’s chapter references. It has no confusion and black holes however.
Here by the way, is Einstein’s preface. It states fairly clearly that this is the “dummies guide to relativity”. Attacking inaccuracies and problems with it is thus not a valid criticism of the theories, but at best valid criticism of Einstein’s abilities at communicating with non-physicists.