Real frame (strong issue)

1. Jul 22, 2006

Born2Perform

A twin is on a spaceship, the other on the earth.
first twin accelerates and get distant form the earth, we know he is moving.
He dies in the spaceship and his son takes control of it.
Now, for his son the system is linear, he does not know the spaceship is moving, and he has not a possibility to discover it.

Halls of ivy said that:
The statement "he has not a way to discover the truth, that his ship is moving" is incomplete. Relative to what frame of reference? His ship is moving relative to some frames of reference, not moving, relative to others (in particular, a person is alway "not moving" relative to his own frame of reference). It simply isn't true to say it is "the truth, that his ship is moving".

It was good for a week, but i think there's a bug: Nobody can deny that the ship is moving, at least you can say it is or it is not relative to some frame of reference. But,
Have you cancelled the acceleration? In a moment of time it happened, for any frame.
And, motion depends from frame to frame, but cannot a frame of reference be wrong? the ship is definitely moving, relative to nothing.

2. Jul 22, 2006

MeJennifer

No, it is not moving relative to nothing.
He is simply moving in space-time, and so is his uncle.

3. Jul 22, 2006

Born2Perform

So you are according that the relativity principle is a fallacy?

4. Jul 22, 2006

MeJennifer

How can something moving relative no nothing be related to relativity. It takes at least two to tango.

With regards to the "relativity principle", you don't need in GR.
It is sufficient to have a metric and a description on how space-time curvature and matter relate.

By the way what do you understand the relativity principle is?

Last edited: Jul 22, 2006
5. Jul 22, 2006

Staff Emeritus
The only motion that counts is the relative motion between the son and his uncle. Both of them are currently unaccelerated according to the statement of the problem, so they are inertial, and each of them is entitled to regard himself as being at rest, according to relativity. As the problem is stated, the spaceship has not turned around, so that if son and uncle communicate by radio, each of them will see the other's coordinates as Lorentz transformed relative to himself.

The son presumably has a record of how much time has passed on the ship since his father set out (we ignore the period of acceleration for simplicity, but if necessary it can be included at the cost of some complexity). Now the son sends this time length in a message to his uncle, and the uncle sends his own elapsed time to the son.

And both of them say "Wow, it took longer for him than it has taken for me!"

Last edited: Jul 22, 2006
6. Jul 22, 2006

MeJennifer

Well let's drill down a bit:

A and B are both in a spacecraft in an inertial frame. A and B are going to travel away from the spacecraft in opposite directions. Both are instructed to accelerate a for t seconds and then continue with a constant speed of s. Both A and B get an additional the instruction that as soon as their distance from the spacecraft is x to send a digitized message as to what their chronometer indicates as elapsed time. Their chronometers are synchronized, A leaves from the front and B leaves from the back. Both are instructed to accelerate a for t seconds and then continue with a constant speed of s.

Now are you claiming that when A and B get their respective messages the time will differ with the one they sent?

7. Jul 22, 2006

Born2Perform

Tell me this:

According with my brain, the spaceship is or isnt moving in spacetime?

If it is, and the son-uncle system is symmetrical, does not mean that there is an absolute motion, that there is a truth but in a symmetrical system we cannot discover it?
You cannot say no because relativity principle says no, here i put in discussion the principle itself.

8. Jul 22, 2006

JesseM

The phrase "moving in spacetime" is not usually used in relativity, since from the perspective of 4D spacetime there is no movement in the usual sense, just various worldlines embedded in spacetime like lines on a 2D piece of paper or strings embedded in a 3D block of ice. There is no absolute sense in which either the ship or the earth is moving, you can pick a frame where the earth is moving while the ship is at rest or a frame where the opposite is true, the laws of physics will work the same way in both frames.

9. Jul 22, 2006

MeJennifer

Any object is always moving in space-time, except for the limit condition of a space-time singularity.

The whole problem with SR is that it is a theory that is completely irrelevant to our existing space-time.
Our space-time has matter distribution, which is a map of reality!
To apply SR in the real universe would mean that you question this reality and are prepared to apply linear transformations, rotations, or even deformations of space-time to "make it work".

All this endless comparing of how frame X sees what frame Y does and vice versa is all due to simple coordinate transformations. There is no objective reality to it.
It is like wondering "how come in the English word "yes" is different in Hungarian and vice versa.

10. Jul 22, 2006

HallsofIvy

Perhaps you could explain what your brain means by "moving in spacetime". Since "spacetime" includes both space and time, an object moving in space corresponds to a single path in "spacetime"

I can say "no" because nothing you have said implies "absolute motion". Each party, son or uncle, sees the other moving relative to himself. If you are questioning the very concept of "relative motion", that is based on experimental evidence (and, except for electro-magnetic phenomena he did not know about, goes back to Galileo). If you want to "question" it, you will need to reference an experiment that contradicts it.

11. Jul 22, 2006

Born2Perform

i understand your rationale, but i'm convinced in something more fundamental:

-------
A body is accelerating.
is it or is it not moving?

-------

and don't say: "according to which frame of reference?"
it's not physics its pure logic, this is the core of my doubt.

Last edited: Jul 22, 2006
12. Jul 22, 2006

MeJennifer

I know that you don't like to hear it but it does depend on the frame of reference.
But if you ask is a curved timeline always curved in space-time then the answer is yes.

13. Jul 22, 2006

Born2Perform

As hight school student i guess i will not undersant this for some years. i don't catch you rationale.

Last thing:
is there a probability that i could be right?
is possible that the sentence:
could be right, or this possibility doesn't exists?

if it does not, i'll have my soul in peace until i'll reach university, if it could be i will think to it more deeply.
thanks.

14. Jul 22, 2006

MeJennifer

Well let me give you an example of a body that is accelerating but not moving in a particular frame of reference.
It is when you stand with your feet on the earth. You are in fact accelerating upwards! The (mostly) electro-magnetic forces accelerate you, and you can feel it as well.

15. Jul 22, 2006

Born2Perform

I'm practising a force upwards, but accelerating???
and however forces that i can't feel are "feelable" with some machine.

saying
is like to say 1+1=2, its Aristoteles logics!
i never have been more certain of something than now.

Really nobody of you feels to say that i could be right, also with a small, or ridiculous probability?

16. Jul 22, 2006

JesseM

From the perspective of any given coordinate system, if an object is accelerating in that coordinate system (ie its coordinate velocity is changing with coordinate time), then of course it must also be moving in that coordinate system (its coordinate position is changing with coordinate time). And if you stick to inertial coordinate systems as is usually done in special relativity, then if something is accelerating in one inertial coordinate system, it is accelerating in all coordinate systems. However, if you allow non-inertial coordinate systems, something which is accelerating in one coordinate system may be at rest or moving at constant velocity in another.

Last edited: Jul 22, 2006
17. Jul 22, 2006

MeJennifer

Well with the proper coordinate systems one can make an elephant out of a monkey.
What matters, at least to me, is what is the significance to reality.

While inertial movements are indeed relative, it is different for movements that are not inertial.

For instance to deny that a rocket leaving our earth is accelerating because all the objects in the whole universe could be accelerating in the opposite direction is just plain silly.
Think about four rockets leaving earth in a plane of opposite directions, north, south, east and west. Now the rockets may not move because of the relativity principle?

Space-time is absolute, so if something moves by a (non gravitational) force, then it is a curved timeline in space-time.

18. Jul 22, 2006

Staff Emeritus

Isn't this a little confused? First you say A and B are to send messages, and then you ask aboout the messages they receive. And you don't say whether x is before or after they stop accelerating. I am going to say after.

So both of A and B have relative speed s with respect to the ship and are currently inertial when they send or receive their messages. The ship is also inertial. So each of A & B sees ship length L_S as shorter, depending on s, and the ship time T_S will be seen by A and B to be longer also depending on s. Since A and B, although in different directions, have the same speed relative to the ship, they will experience the same transformation in seeing the ship data.

And what will the ship see from A's and B's messages? Exactly the same! L_A and L_B will both be less than L_S (assuming it's some common length like a meter stick that they agreed on back when both A and B were on the ship. And T_A and T_B will both be greater than T_S, with the same caveat.

The point is that all inertial systems are equal, and if one of a speed related pair sees the other's data treansformed, the second of the pair sees exactly the same transformation for the data from the first. To break that symmetry you have to accelerate. But your acceleration happened before they started comparing, so it doesn't factor in.

19. Jul 22, 2006

HallsofIvy

Yes, that's true. And if you kept asserting that 2+ 2= 5, nobody would feel like saying you could be right "also with small, or ridiculous probability" either!
I might also point out that if you assert
then I can only include that you do not know "Aristoteles logics". Neither of those statements has anything to do with Aristotelian logic.

I can also conclude that you do not know what acceleration is. It is quite possible for a body to be moving with a non-zero (constant for simplicity) acceleration and yet, at a given instant, have 0 speed (i.e. not be moving) relative to some inertial coordinate system. Of course, it follows, from the definition of "inertial coordinate system" that an accelerating object can only momentarily motionless relative to a specific inertial coordinate system. However, it follows that such an object is, at any instant, motionless relative to some inertial coordinate system. And, of course, if we drop the "inertial", we can always assert that an object is motionless relative to its own coordinate system. Asserting that an accelerating object "must be moving" doesn't prove there exist "absolute" motion because acceleration itself must be relative to some coordinate system.

And, finally, just asserting that YOU don't understand relativity does not prove that it is wrong. All of relativity is based on experimental results- the only way to dis-prove a physical theory is to demonstrate experimental results it cannot explain. Can you do that?

20. Jul 22, 2006

JesseM

Are you familiar with the concept of "diffeomorphism invariance" in GR? My understanding is diffeomorphism invariance means that because of the way the laws of GR are formulated, virtually any coordinate system you can think of (except perhaps for poorly-behaved ones where the same event is assigned multiple sets of coordinates or problems along those lines) is equally good, the same laws of physics will be obeyed in all of them (see http://www.advancedphysics.org/forum/archive/index.php/t-3532.html of how using GR, you can analyze the problem from the point of view of a coordinate system where the twin who accelerates (from the point of view of inertial coordinate systems) is at rest throughout the entire trip, and the G-forces she feels during the phase of the trip where inertial observers say she's accelerating are explained in this coordinate system by the creation of a "uniform gravitational field" (although this term should be taken with caution, as the page explains) during this phase of the trip:
If you still find the analysis from the perspective of this coordinate system "silly", despite the fact that the same laws of GR are being obeyed in it, can you explain whether "silly" is just an aesthetic opinion or whether it has some more rigorous physical meaning? After all, someone might also consider it "silly" to use an inertial frame where the whole earth is moving at high speed while the rocket the twin is riding is at rest, but hopefully you'd agree all inertial frames are equally valid from the perspective of SR, and the situation with different non-inertial coordinate systems in GR seems analogous to this.

Last edited by a moderator: Apr 22, 2017
21. Jul 22, 2006

MeJennifer

"... she is forced to assume that a uniform "gravitational" field suddenly permeates the universe"

So you are not really sure that every time a space-shuttle takes off we could not instead have some uniform gravitational field permeating the universe instead? Sorry, but than one might as well believe that some invisible pink unicorn is suddenly deforming space-time.

Sorry, but I guess I am a simpleton, I simply don't believe that uniform "gravitational" (whatever the double quotes supposed to mean) fields can suddenly permeate the universe as soon as a rocket takes off. Do you believe that?

It is simply amazing to me what people want to offer not to "hurt Einstein's feelings", it is almost like religion.
Again inertial worldlines are relative, no problem with that whatsoever, but non-inertial worldlines, which are caused by non gravitational forces, are not.
But, again, I apologize, I am a simpleton.

I don't.

Last edited: Jul 22, 2006
22. Jul 22, 2006

JesseM

All I can say is that if you adopt this alternate coordinate system, diffeomorphism invariance means the laws of physics will be no different in this system. Did you look at http://www.einstein-online.info/en/spotlights/background_independence/index.html [Broken] explaining diffeomorphism-invariance and background independence?

Your argument seems to just be one of aesthetic distaste for the analysis from a particular coordinate system, but that is obviously not a rigorous way of deciding which coordinate systems are acceptable and which are not. A critic of special relativity might come up with a similar aesthetic argument against the equivalence of different inertial frames--they might say something like, "surely you don't expect me to believe that if I am flying away from the earth in a rocket moving at constant velocity relative to the earth, it is actually the earth, the sun, in fact the entire galaxy which are moving away from the rocket while the rocket is standing still? Ridiculous!" How would you respond to such an argument? I think the only way to respond would be to point out that the criterion physicists used to decide when coordinate systems are "equivalent" is based on checking whether or not the laws of physics work the same way in the different coordinate systems--this is why in special relativity non-inertial coordinate systems are not equivalent to inertial ones, because if you tried to apply the usual non-tensor equations of SR that work in inertial systems like the rule for time dilation as a function of coordinate velocity, you'd get the wrong answers to physical questions like how much a clock will tick between two events on its worldline. Likewise, electromagnetic fields will obey the non-tensor form of Maxwell's laws in all inertial coordinate systems, but not in non-inertial ones. So this is why physicists say that all inertial coordinate systems are equally valid in SR, but that non-inertial ones are not equivalent to inertial ones. But when you go to GR, you find that the laws of physics expressed in tensor form will work just the same way in all coordinate systems, including non-inertial ones, so if you apply the same criterion you should conclude that there is no reason to prefer one coordinate system over another.

If you disagree with this reasoning, does that mean you disagree with the rule that if the laws of physics work the same way in different coordinate systems, these coordinate systems are equally valid? If you do reject that rule, then I don't think you have any basis for saying the argument of the SR skeptic I imagined above is wrong, and in fact I don't think you have any rigorous rule for deciding which coordinate systems are valid and which aren't, it would seem to be based on nothing but your own aesthetic preferences (if you do have a rigorous rule that differs from the one used by physicists, then please state it).
If you read the rest of that page, they explain the reason for the scare quotes. A "uniform gravitational field" is distinguished from a regular gravitational field because it does not involve matter/energy curving spacetime, not all physicists would even use the term "gravitational field " to describe this.
What does it mean to "believe" or "disbelieve" something which is not a physical fact, but which depends on your choice of coordinate systems? If the relative velocity between me and the earth is 0.5c, do you "believe" that I am at rest while the earth is moving away from me at 0.5c, as would be true in my rest frame? Do you "believe" that my current position along the x-axis is x=203.5 meters, as would be true in a coordinate system whose origin is 203.5 meters away from me and whose x-axis crosses my current position? These seem like meaningless questions to me, I think you are taking an overly concrete approach to coordinate-based statements. The only thing I "believe" that's relevant here is that all the laws of physics, when stated in terms of tensor equations, will obey exactly the same equations in a coordinate system where the travelling twin was at rest throughout the journey as they do in a coordinate system where the earth-twin was at rest between the time the travelling twin left and came back, and that this is the criterion that physicists use to decide whether different coordinate systems are equally valid.
I think you may have misunderstood me--I was just saying "hopefully you'd agree" with the statement "all inertial frames are equally valid from the perspective of SR", I wasn't asking whether you agreed with the separate statement that "the situation with different non-inertial coordinate systems in GR seems analagous to this", that second part was my own assertion. It's analogous in the sense that exactly the same criterion is used to decide whether different coordinate systems are equally valid in both cases--namely, the criterion of whether the laws of physics obey the same equations in the different coordinate systems. Again, if you have an alternate criterion that's just as rigorous, please describe it; if you don't, then the only conclusion is that your judgements about the validity of different coordinate systems are based on your own personal aesthetic criteria.

Last edited by a moderator: May 2, 2017
23. Jul 23, 2006

MeJennifer

Ok so, let's take a coordinate system of space-time where a geodesic is a straight line. Now let's go back to the spaceship taking off from the landing platform, and accelerating away from earth.
Would you then agree or disagree that the principle of relativity holds in this case? Can we say who accelerated or is it all relative?

Last edited: Jul 23, 2006
24. Jul 23, 2006

Staff Emeritus
Special relativity is what is called a "kinetic" theory; this means it has speed built into it (via c soming into the metric); that means you can solve "pure speed" problems straight out with just algebra and arithmetic. But accelerations are not so easy; they are not built into special relativity and in addition to the limits and calculus you always have to use for acceleration, you have also the formalism of "comoving frames" which is necessary to do relativitstic calculation for accelerating objects.

That said, the answer to your question is that accelerations are not relative; the people on the ship feel the acceleration and they are not inertial. There are length contractions and time dilations that apply to them (relative to the launching pad) but they are calulated using those comoving frames. In this case what the people on the ship see is not the same as what the people on the launching pad see.

25. Jul 23, 2006

MeJennifer

Well I agree with you.

By the way are you suggesting that when we assume that geodesics are straight lines in space-time it must be true that we are talking about a flat space-time?

Last edited: Jul 23, 2006