Cause of Inertia

[A Thousand Pardons]

Implict, yes. Explicit, no.

I would have said explicit, yes, but that's just me.

Here follows what may be a flaw in Einstein's theory, or, is it not a flaw, and if not, please explain why.

The pendulum in the elevator experiences the exact same degree of
accelerational force at all points in its swing.

That's not quite true (see the discussion on this board about the rope paradox), but it's true enough for these purposes.

If the elevator is accelerating at one gee and the gravitational field is
one gee there appears to be a discrepancy in the forces "felt" by the
pendulum in the two frames of reference. Yet Einstein postulates there is
none. Why is this so?

Einstein was well aware of the discrepancy, he did not postulate that there was none. Just as before, above, the discrepancy is small enough that it doesn't matter in the case at hand.

[Grey]

But Grey mentioned the Higgs Boson. While Googling gives few link-ups between this and Mach's Principle, there are a few more with regard to the Higg's Field.

The link you'd found is more or less what I was suggesting. That is, if it's an interaction with the Higgs boson that's the cause of inertia, then it would seem to be a purely local phenomenon. However, since one can view the Higgs partical as a disturbance in the Higgs field (and indeed, I believe that it's possible for there to be a Higgs field without a particle manifestation, though that's not the way most particle physicists are betting), one could at least postulate that the field has whatever properties it has because of interactions with all the matter in the universe. It seems unlikely to me, but that doesn't mean that it isn't the way the universe works.

I do wonder if the reason for the small number of references is that Mach's Principle is more of a philosophical position, whereas those searching for the Higgs particle are hard-core particle physicists, who may be less concerned about philosophical matters. But that's pure speculation on my part.

[Evan]

he did not postulate that there was none.

Yes he does.

Quote from Einstein: "Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time."

Further he states: "It is not possible by experiment to distinguish between an accelerating frame and an inertial frame in a suitably chosen gravitational potential, provided that the observations take place in a small region of space and time"

Is he right? Why?

[Grey]

Yes he does.

Quote from Einstein: "Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time."

Further he states: "It is not possible by experiment to distinguish between an accelerating frame and an inertial frame in a suitably chosen gravitational potential, provided that the observations take place in a small region of space and time"

Is he right? Why?

Yes he is. The "suitably chosen gravitational potential" that would be equivalent would be that created by an infinite flat plane, which gives an attractive force that doesn't vary in direction or fall off with distance.

Of course, there aren't any such objects, but since he's talking about a small region, any gravitational field that could be considered constant within that region would work, too. How well the two situations agree depends on just how quickly the real gravitational field varies, and how small you're willing to make the region of interest.

[A Thousand Pardons]

he did not postulate that there was none.

Yes he does.

No, I disagree. As I said before, he was aware of the discrepancy.

Quote from Einstein: "Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time."

That's not exactly "postulating"

Further he states: "It is not possible by experiment to distinguish between an accelerating frame and an inertial frame in a suitably chosen gravitational potential, provided that the observations take place in a small region of space and time"

Is he right? Why?

Yes, the key words are "small region of space and time". If you limit your measurements to a small enough region of space and time, you won't be able to measure the difference. If you don't limit it, then you would be able to measure the difference. Einstein's point in saying it that way is essentially the same point that you are making.

As I say, he was aware of the difference.

[Evan]

There is a reason why you can't determine by experiment what frame of reference you are in and it isn't because the effects are too small to measure. The reason is not given by Einstein in his explanation but pertains nonetheless.

The principle of Equivalence means just that, equivalence. Not almost equivalent.

[A Thousand Pardons]

There is a reason why you can't determine by experiment what frame of reference you are in and it isn't because the effects are too small to measure. The reason is not given by Einstein in his explanation but pertains nonetheless.

The principle of Equivalence means just that, equivalence. Not almost equivalent.

That's right. It has nothing to do with the pendulum thought experiment.

[worzel]

There is a reason why you can't determine by experiment what frame of reference you are in and it isn't because the effects are too small to measure. The reason is not given by Einstein in his explanation but pertains nonetheless.

The principle of Equivalence means just that, equivalence. Not almost equivalent.

As someone pointed out, it is exactly equivalent to an infiinite flat plane with finite gravitional pull everywhere, or in my own words above, an infinitely large planet with finte g.

[Grey]

There is a reason why you can't determine by experiment what frame of reference you are in and it isn't because the effects are too small to measure. The reason is not given by Einstein in his explanation but pertains nonetheless.

I'm curious. What is this other reason you're suggesting?

[Evan]

????

The reason not given by Einstein is because of the difference in time dialation in a gravitational field vs the constant time dialation in an accelerating frame. In a gravitational field time is more dialated the deeper into the gravity well you go. This has the effect of equalizing the measured swing of a pendulum or the velocity of a falling body. It is tied to the concept of simultanaeity. Ironically, it is the one difference between the frames that makes them the same. He intentionally ignores the geometric difference between the frames caused by the radial distribution of gravity vs the rectilinear acceleration in the moving frame. Einstein glossed over that point as being self evident.

[ToSeek]

Given instruments of unrestricted sensitivity, I can think of at least two ways of figuring out whether you're in an accelerating elevator or in a gravitational field, with the given example being one of them.

Care to explain?

Basically, in an accelerating frame, the force of acceleration will be the same everywhere in the elevator. In a gravitational frame, there are two differences:

1. There will be less gravitational force higher in the elevator than lower (this seems to be what you were alluding to).

2. Since the source of gravity is effectively a point, the direction of gravity will be slightly different from one side of the elevator to the other.

[A Thousand Pardons]

The reason not given by Einstein is because of the difference in time dialation in a gravitational field vs the constant time dialation in an accelerating frame.

That's not strictly true. See the rope paradox discussion that I mentioned earlier.

In a gravitational field time is more dialated the deeper into the gravity well you go. This has the effect of equalizing the measured swing of a pendulum or the velocity of a falling body. It is tied to the concept of simultanaeity. Ironically, it is the one difference between the frames that makes them the same. He intentionally ignores the geometric difference between the frames caused by the radial distribution of gravity vs the rectilinear acceleration in the moving frame. Einstein glossed over that point as being self evident.

In the popular expositions, yes. Why wouldn't he? And even then, he didn't really ignore it, as I mentioned before. His wording ("in a small region of space and time") allows just enough reference to it to be accurate without having to go into the gory details.

[worzel]

The reason not given by Einstein is because of the difference in time dialation in a gravitational field vs the constant time dialation in an accelerating frame.

As far as I understood it, the gravity field / acceleration equivalence menas that in the elevator clocks below you run slow while clocks above you run fast. You can also come to this conclusion by considering the acceleration as an ever increasing number of ever smaller lorentz boosts, you get the same answer.

[Evan]

That is correct. In the gravitational field the clock runs slower the further into the field it is. Also, any clock used to measure the period of the pendulum swing will be affected depending on where the swing is measured. Same for a falling body. As it falls into the well time slows in direct proportion to the increase in gravity.

In the accelerating frame time dialation is equal throughout the frame. It is of course increasing as the frame accelerates but it increases equally at all points. A clock used to measure the pendulum swing experiences the same time dialation regardless of where it is in the accelerating frame.

[Grey]

In the accelerating frame time dialation is equal throughout the frame. It is of course increasing as the frame accelerates but it increases equally at all points. A clock used to measure the pendulum swing experiences the same time dialation regardless of where it is in the accelerating frame.

I believe this is inaccurate. Observers at the top and bottom of an accelerating elevator will agree that the top clock runs faster and the bottom clock runs slower. The time dilation from gravitational/acceleration effects is based on the potential, which is different at different heights in the elevator, regardless of the fact that the force experienced is the same. Similarly, if there were an infinite flat plane, the time dilation closer to it would be more pronounced than that farther away, even though the force would remain constant.

[A Thousand Pardons]

That is correct.

I believe it is correct too but I think it is the opposite of what you say here:

In the accelerating frame time dialation is equal throughout the frame. It is of course increasing as the frame accelerates but it increases equally at all points. A clock used to measure the pendulum swing experiences the same time dialation regardless of where it is in the accelerating frame.

[Evan]

"The time dilation from gravitational/acceleration effects is based on the potential, which is different at different heights in the elevator"

What potential? When an object is dropped in the accelerating elevator it doesn't fall into a potential well, it is left behind.

[A Thousand Pardons]

What potential?

Remember the principle of equivalence

[Evan]

The principle of equivalence does not mean the two frames of reference are identical. Obviously they are not. It does mean that no test may be performed to distinguish between them and that is so. The limiting factor that prevents distinguishing any difference is imposed by the contraints of simultaneity.

[worzel]

Obviously they are not.

There's that word "obviously" again

[A Thousand Pardons]

The principle of equivalence does not mean the two frames of reference are identical.

No, but there is a difference in potential. Think about a ball held near the top, and released. It will pick up speed in that frame, and energy, as it drops from a higher potential to a lower one.

[Evan]

Well, actually the frame picks up speed relative to the ball. It's the frame that has energy added to it, not the ball (until it hits the floor and is also accelerated). Imagine standing in the airlock of a spaceship accelerating at one gee and throwing the ball out the hatch. It will arc away and appear to curve "down" as if it were under the influence of gravity. But it isn't.

This isn't just semantics either. There is a difference in the time dialation in the two frames. It's that difference that equalizes the measured results.

[A Thousand Pardons]

This isn't just semantics either.

I'll agree there.

There is a difference in the time dialation in the two frames.

Not according to the experts.

[Evan]

Still disagree, and so do the experts. If you have a clock on the ceiling of the accelerated elevator producing flashing light pulses a detector on the floor will measure a pulse rate that is doppler shifted by the motion of the elevator to produce a shorter period. In the stationary frame in a gravitational field the same period is produced by the variance in time dilation instead of doppler shift. The clock at the top of the elevator runs faster than at the floor because of the variance of time dilation that doesn't exist in the accelerating frame. The net result is the same for both observers but the mechanism is different.

See the section on Principle of Equivalence.

http://www.astro.ucla.edu/~wright/relatvty.htm

[Grey]

The principle of equivalence does not mean the two frames of reference are identical. Obviously they are not. It does mean that no test may be performed to distinguish between them and that is so.

You're saying that there are two situations which are observationally indistinguishable, but then claiming that they are obviously different? How can we tell that they are different?

Still disagree, and so do the experts. If you have a clock on the ceiling of the accelerated elevator producing flashing light pulses a detector on the floor will measure a pulse rate that is doppler shifted by the motion of the elevator to produce a shorter period. In the stationary frame in a gravitational field the same period is produced by the variance in time dilation instead of doppler shift. The clock at the top of the elevator runs faster than at the floor because of the variance of time dilation that doesn't exist in the accelerating frame. The net result is the same for both observers but the mechanism is different.

I'll agree that the mechanism is different depending on which frame of reference you choose. However, the point of the principle of equivalence is that, since I can't tell observationally which is which, I'm free to decide whether my frame of reference is accelerating or in a gravitational field, or perhaps some combination of the two. Remember that the indistinguishability is a postulate here, and the argument you're describing was the one used to show that there had to be gravitational time dilation, so that you wouldn't be able to tell the difference between these two cases.

[Evan]

Grey,

We know the two frames are different. We are outside of them. It is the observer in the frame that can't tell the difference. If you go back to the original question I posed I asked what it was that accounted for the inability of the observer to distinguish the difference. The difference between the two frames is time dilation due to gravity which, as I have said, makes them seem the same. This is an important point that is not explained or touched on by Einstein in his original "Man in the Chest" thought experiment. He was certainly aware of it but he oversimplified his explanation.

[Grey]

We know the two frames are different. We are outside of them. It is the observer in the frame that can't tell the difference.

And what is it that makes choosing an outside frame of reference motionless with respect to the one in the "real" gravitational field better than choosing one motionless with the one that's "obviously" really accelerating? Pushing it to an outside observer doesn't really help solve the problem, since under general relativity it's still technically just as appropriate to choose an accelerated outside observer as a non-accelerated one.

To be fair, the first one has the advantage that there's this obvious Earth to account for the apparent gravitational field of the stationary observer, and we can see how the field varies relative to it, but that's a decidely nonlocal consideration, and we can always choose to postulate an infinite flat plane a very long ways away to account for any extra apparent gravitational forces or accelerations.

We can also see that the "obviously" accelerating reference frame seems to be accelerating relative to the "fixed stars", whereas the "stationary" one is not (another nonlocal observation, of course), which may bring us back to the original post here. If there's something special about not being accelerated relative to the "fixed stars", are they somehow responsible for this, as Mach's Principle suggests?

The difference between the two frames is time dilation due to gravity which, as I have said, makes them seem the same. This is an important point that is not explained or touched on by Einstein in his original "Man in the Chest" thought experiment. He was certainly aware of it but he oversimplified his explanation.

I'm not sure I agree. That is, I know that the two observers will disagree about the mechanism involved, but I don't think Einstein glosses over it. In fact, I believe that it was this very thought experiment that first led him to suggest that gravitational time dilation would be observed so that the two cases would remain indistinguishable, even before he had finalized the general theory of relativity.

[Evan]

And what is it that makes choosing an outside frame of reference motionless with respect to the one in the "real" gravitational field better than choosing one motionless with the one that's "obviously" really accelerating?

That is Einstein's choice. His thought experiment assumes unrealistic ideal conditions so as to consider only the matter at hand. A perfectly valid approach. However, when doing so it is then essential to consider all contributions to the matter at hand however trivial. As I said before about the Casimir effect, it's not how well the bear dances, it's that he dances at all. When assuming ideal conditions we have the luxury of assuming infinitely sensitive and perfectly accurate tools. We can and must deal with conditions that cannot be practically measured. I don't think that Einstein used this particular thought experiment to help formulate his ideas on time dilation. The particular difference between the two frames of reference should have been glaringly obvious to him. I have seen it and certainly don't claim to be in his league. He skips the geometry issue as being self evident, which it is. He cannot skip the dilation issue as it does not depend on geometry and applies even to a one dimensional consideration of the problem.

Here is the translation of Einstein's original thought experiment. It is intended to illustrate the principle of Equivalence. It is grossly oversimplified. He does cop out a bit with the word "approximately" but I don't feel that excuses the ommision of the effects of dilation. After all, he is speaking about relativity. It also would do well to remember this is around 1916. The part I have placed in bold is the oversimplification.

Imagine a large portion of empty space, so far removed from stars and other appreciable masses, that we have before us approximately the conditions required by the fundamental law of Galilei.

It is then possible to choose a Galileian reference-body for this part of space (world), relative to which points at rest remain at rest and points in motion continue permanently in uniform rectilinear motion. As reference-body let us imagine a spacious chest resembling a room with an observer inside who is equipped with apparatus.

Gravitation naturally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling of the room.

To the middle of the lid of the chest is fixed externally a hook with rope attached, and now a "being" (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest together with the observer then begin to move "upwards" with a uniformly accelerated motion. In course of time their velocity will reach unheard-of values -- provided that we are viewing all this from another reference-body which is not being pulled with a rope.

But how does the man in the chest regard the process?

The acceleration of the chest will be transmitted to him by the reaction of the floor of the chest. He must therefore take up this pressure by means of his legs if he does not wish to be laid out full length on the floor.

He is then standing in the chest in exactly the same way as anyone stands in a room of a house on our earth.

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. The observer will further convince himself that the acceleration of the body towards the floor of the chest is always of the same magnitude, whatever kind of body he may happen to use for the experiment. My words here: Including light pulses...

Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time.

The fact that the light pulses are doppler shifted is extremely significant to the theory. Einstein places us in the inertial frame of reference and therefor we need to be able to account for the reasons the observer cannot see a difference.

[worzel]

The chest together with the observer then begin to move "upwards" with a uniformly accelerated motion.

This is the phrase that I think is glossing over the details. When a rigid body remains uniform in its own frame it can not be accelerating uniformly in an another frame (see ATP's earlier link to a thread on ropes and planes).

A lorentz boost makes clocks in the direction of the boost leap forward proportionally to their distance from you (one way to resolve the twin paradox). Acceleration is just an infinite series of infinitely small boosts which results in the clocks above you smoothly running faster than yours rather than leaping periodically. I think that relies on the "clocks postulate" but can't remember what that is.

[A Thousand Pardons]

Here is the translation of Einstein's original thought experiment. It is intended to illustrate the principle of Equivalence. It is grossly oversimplified. He does cop out a bit with the word "approximately" but I don't feel that excuses the ommision of the effects of dilation. After all, he is speaking about relativity. It also would do well to remember this is around 1916.

That passage is from his popularization of relativity, Relativity: The Special and General Theory which was written around 1920 I think and revised many times.