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Intertial & Non-Intertial Frames


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Showing 76-100 of 209 posts in this discussion
In reply to an earlier post on Jun 20, 2012 3:47:49 PM PDT
Last edited by the author on Jun 20, 2012 3:56:27 PM PDT
tom kriske says:
i'll have to raise issue with your disagreement. consider a thought experiment wherein your rocket ship leaves earth via overcoming escape velocity [noninertial frame], then moves at constant velocity toward the sun[inertial frame], then gets caught in suns gravity well and accelerates toward it [noninertial], then you break away after going once about it and end up in uniform motion away from it [inertial].

mathematically you are perfectly capable of modeling this motion by a series of transformations, each acting on the body of the rocket from liftoff to deep space.

inertial frames absolutely can be transformed into noninertial ones, and back again.

edit: this from a wiki on noninertial frames - 'Measurements with respect to non-inertial reference frames can always be transformed to an inertial frame, incorporating directly the acceleration of the non-inertial frame as that acceleration is seen from the inertial frame.'

In reply to an earlier post on Jun 20, 2012 4:54:47 PM PDT
arpard fazakas,

Would you not agree that the gravitational field being extremely weak still implies that gravitational field is still at play?

In reply to an earlier post on Jun 20, 2012 8:42:25 PM PDT
Last edited by the author on Jun 20, 2012 8:48:42 PM PDT
D. Colasante says:
af >> ...an inertial frame which is moving at the speed of light... Such frames don't exist, and make no sense

It's fair to consider reference frames an abstraction. Real or not, a variety are represented in Minkowski space. The light-like intervals are fascinating to me because it is upon these that E- and G-fields are manifest. (I argue this is because they are the same field.)

In addition, the purely space-like interval seems relevant to certain phenomena such as quantum tunneling. Considered a requirement for stellar nucleosynthesis, particles are said to exist to varying degrees over a field of locations at once (even through obstacles). Such a field might be thought equivalent to instantaneous (space-like) distribution of the particle. One might also consider it meaningful to an electron in its orbital.

In reply to an earlier post on Jun 20, 2012 9:05:35 PM PDT
In fact, no frames actually exist! They are just aids to calculation, so you choose the one most convenient.

In reply to an earlier post on Jun 20, 2012 9:16:05 PM PDT
SCL:

If they ever manage to quantize gravity, then I suppose you could--in principle--have a situation in which gravitons were hitting the frame one at a time, just as photons can be generated at intensities this low. In which case, then the time between graviton arrivals would seem to be purely inertial, even though the fields are infinite in reach.

Also, in the Big Rip scenario, I can imagine big 'gaps' of observational horizons that contained no real particles, whatsoever--once inflation has had the opportunity to complete its business.

In reply to an earlier post on Jun 20, 2012 9:25:12 PM PDT
tom kriske says:
dc, given your open affection for null surfaces, i would strongly encourage you to explore spinor and twistor analyses. cartan introduced isotropic vectors, aka spinors, in the 20's[i think] as an interesting outgrowth of his researches into general transformation groups. weyl came upon them, more or less contemporaneously, pondering certain 2->1 mappings in the theory of rotation groups.

twistors, among other things, have been shown to aid in, and sometimes furnish, the solution of certain equations which arise naturally in general relativity.

i'd think you'd take to it like fish to a taco shell.

In reply to an earlier post on Jun 21, 2012 5:44:55 AM PDT
tom kriske says:
that's exactly right, pick the frame that makes the physics easiest to work with.

In reply to an earlier post on Jun 21, 2012 7:53:55 AM PDT
A spaceship in the sun's gravitational field moving at constant velocity towards the sun is not in an inertial frame of reference, as the astronaut can easily demonstrate to herself by noting that light rays moving neither parallel nor antiparallel to her rocket follow a curved path, and light coming from the sun is redshifted. It's "caught in the sun's gravitational well" the whole time. Likewise when it's moving away from the sun at a constant velocity, at least until it's so far away that the strength of the sun's gravitational field becomes vanishingly small.

In reply to an earlier post on Jun 21, 2012 7:54:47 AM PDT
Yes but at some point it may become so weak that it's below the limit of detection. In that case for all practical purposes we're now in an inertial frame.

In reply to an earlier post on Jun 21, 2012 7:56:19 AM PDT
An inertial frame moving at the speed of light would imply that objects with mass could be moving at the speed of light in this frame, which is a physical impossibility. Just one reason why inertial frames moving at the speed of light are not possible.

In reply to an earlier post on Jun 21, 2012 7:57:17 AM PDT
Nonsense. Frames are defined by well-described processes and exist. Please refer to Einsteins's original paper on special relativity for instructions on how to define inertial frames.

In reply to an earlier post on Jun 21, 2012 10:44:12 AM PDT
tom kriske says:
<<that's exactly right, pick the frame that makes the physics easiest to work with.>>
arpard fazakas says:
<<Nonsense. Frames are defined by well-described processes and exist. >>

Hmm.. It seems we have a slight difference of opinion!

My considered opinion is that af's processes might exist, but not the frames, themselves: There are no coordinate axes conveniently drawn for us in space-time. We must provide them ourselves, and it would be foolish to let ourselves be misled by our diagrams.

In reply to an earlier post on Jun 21, 2012 10:56:21 AM PDT
Last edited by the author on Jun 21, 2012 10:57:23 AM PDT
If an observer defines herself as being at rest, then she is in one specific frame of reference with 100% certainty, determined by the physical state of her environment. She can use different coordinate systems to enable calculations, but it doesn't change the underlying nature of the frame of reference. It will either be inertial or noninertial, and if it's noninertial it will be noninertial for certain definite reasons, such as rotation, or presence of a gravitational field.

I think you're confusing coordinate systems with frames of reference. Coordinate systems are mathematical ways of labelling frames of reference. One gets the same answers when one does physics regardless of which coordinate system one uses to do the calculations. In a generally covariate system such as general relativity one gets the same laws of physics from any coordinate transformation and in any frame of reference.

In reply to an earlier post on Jun 21, 2012 11:08:18 AM PDT
Last edited by the author on Jun 21, 2012 11:08:36 AM PDT
tom kriske says:
arp, that doesn't address
the point.

In reply to an earlier post on Jun 21, 2012 11:12:31 AM PDT
Last edited by the author on Jun 21, 2012 11:34:53 AM PDT
Jack Shandy says:
-"light coming from the sun is redshifted. It's "caught in the sun's gravitational well" the whole time. "

Are you claiming that freefall/geodesic motion is not inertial motion? That's a rather weird claim, if you ask me. If I'm falling toward the sun, I'm in my own local inertial frame the entire time during which spacetime curvature is negligible. That light from the sun is redshifted is irrelevant, since the sun does not share my inertial frame. For an inertial frame it is of importance that experiments -done locally- cannot distinguish between my freefall in curved spacetime or my freely floating in Minkowski space. Any local experiment measuring redshift can only compare the frequencies detected at my feet and at my head, otherwise it is not a local experiment anymore.

And the bending of light rays is not measurable either if I restrict the spatial extent of my frame sufficiently (as long it can contain me). Spacetime is locally flat.

In reply to an earlier post on Jun 21, 2012 11:25:23 AM PDT
Agree that one can always define an inertial frame at any point in spacetime, i.e., one which is locally flat, but sometimes the "locally" is so restricted that the locally flat frame is useless for doing physics.

A spaceship moving at constant velocity toward the sun is not in freefall. To be in freefall it would have to be accelerating at a constant rate.

In reply to an earlier post on Jun 21, 2012 11:43:47 AM PDT
Last edited by the author on Jun 21, 2012 11:48:17 AM PDT
Jack Shandy says:
-"A spaceship moving at constant velocity toward the sun is not in freefall. To be in freefall it would have to be accelerating at a constant rate."

Okay, we got some confusion with terminology. I wouldn't confuse freely falling with accelerating. At least not when discussing GR.

Edit: I meant relative velocity is ill defined. Never mind..

In reply to an earlier post on Jun 21, 2012 11:48:05 AM PDT
The sun's gravitational field is sufficiently weak that one can equate free fall and constant acceleration until one gets quite close.

I don't think there's a problem defining velocity with relation to a distant object in special relativity. One chooses as the distant object an observer at rest at the origin of her inertial frame.

In reply to an earlier post on Jun 21, 2012 12:02:33 PM PDT
Last edited by the author on Jun 21, 2012 12:06:10 PM PDT
Jack Shandy says:
-"The sun's gravitational field is sufficiently weak that one can equate free fall and constant acceleration until one gets quite close."

I understand the equality of gravity and acceleration differently: constant acceleration in free space is equivalent with remaining at some fixed gravitational potential.

But I see we have another terminology clash:
You use the word 'acceleration' with respect to some coordinate lattice fixed to the sun, but actually, this is not the acceleration of the observer, but that of the lattice w.r.t. the local inertial frames. I'd reserve the word 'acceleration' solely for 'deviating from geodesic motion'.

In reply to an earlier post on Jun 21, 2012 12:06:34 PM PDT
You've lost me.

My comment about equating free fall and constant acceleration is meant to be taken in the context of gravitation being adequately approximated by Newtonian gravity in the weak gravitational domain, i.e., as long as one isn't too close to the sun.

In reply to an earlier post on Jun 21, 2012 12:19:40 PM PDT
D. Colasante says:
af >> ...inertial frames moving at the speed of light are not possible.

An inertial frame is one which is not accelerating. Therefore an inertial frame may have *any* constant velocity. If such a frame exceeds speed c it is not a "relativistic" inertial frame. Does such a frame not make sense? That's up to you. Do they exist or have any application? I suggested a few. Localities on the other side of an event horizon (moving backward in time??) might be another, obviously theoretical.

I don't see how "Frame c" implies co-moving massive particles.

Recall that you have no problem with frames arbitrarily close to c (e.g. neutrinos). Before denying Frame c, consider that a photon's rest frame exists for zero time (photons don't age) and accompanies it for zero distance (a photon's path length). To the extent that you deny photons' rest frames, I deny photons (not light, photons). The energy quantum transfers by "remote contact".

Said another way: It's time for us to adopt a modern definition of "contact". Instead of the Newtonian notion:

zero length between two particles in space (at a given time),

we should rise to the relativistic generalization that "contact" is:

zero interval between two events in spacetime.

This surpasses the Newtonian definition to include intervals with positive spatial components, thus "remote" contact. It adds all EM interactions to "classical" contact (which is itself, now called into question).

In reply to an earlier post on Jun 21, 2012 12:21:31 PM PDT
Last edited by the author on Jun 21, 2012 12:22:29 PM PDT
Jack Shandy says:
That's what I mean: Newtonian terminology is different from that of GR. The same words mean different things.

But eh, you were talking about measuring gravitational redshift, and bending of light, to determine whether or not your frame is inertial, right? If the Newtonian approximation applies, you won't be able to measure these (with local experiments), and your frame is inertial, even though you are 'accelerating' under gravity (if you are bent on interpreting gravity as a force).

In reply to an earlier post on Jun 21, 2012 12:22:11 PM PDT
Let's say you're at rest at the origin of your inertial frame. In this frame you turn on a source of photons and get zillions of them, each moving at the speed of light. Now define a frame of reference in which one of them is at rest, i.e, one which is moving at the speed of light relative to you. Then you are moving with the speed of light relative to it. Which is impossible.

Since it is impossible for you to move at the speed of light, and it is impossible for a photon to be at rest in any reference frame, it is impossible to have an inertial reference frame travelling at the speed of light.

In reply to an earlier post on Jun 21, 2012 12:25:26 PM PDT
I was replying to a post which claimed that someone moving toward the sun at a constant velocity was in an inertial frame. My claim is that this is not an inertial frame, because it includes a gravitational force, which can be detected by curvature and redshift of light.

In reply to an earlier post on Jun 21, 2012 12:31:21 PM PDT
Last edited by the author on Jun 21, 2012 12:36:33 PM PDT
Jack Shandy says:
Why a constant velocity?

Edit: that's a question for tom kriske..
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Discussion in:  Science forum
Participants:  13
Total posts:  209
Initial post:  Jun 12, 2012
Latest post:  Jul 9, 2012

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