I've shown you the website like six times, Tom. If you don't understand it now, it's no one's fault but yours. - Warren
Prosoothus, The reason I linked you to that textbook is that I can't make the figures in this forum. Could you please read the relevant sections and post specific questions? That book is pretty good--you should be able to understand it. Tom
Tom2, I downloaded it, and browsed through part of it, earlier today. I'll read the part regarding the Twin Paradox later today, and ask questions if I don't understand (or point out mistakes if I do Please Register or Log in to view the hidden image!)
My spin This is such an interesting thread. Its debates such as these that drive science forwards. Sometimes, the "crackpot" turns out to be right, other times, well he/she's just a crackpot. I'm undecided so I'm going to work this through with a small thought experiment... <here I have to refer to my physics textbooks for clarity as to the accepted theorys of relativity> Something jumps out at me here: "All laws of physics are the same in all inertial frames" and "According to a stationary observer, a moving clock runs more slowly than an identical stationary clock by a factor of y^-1. This effect is known as Time Dilation" (in whatever frame of reference stationary is deemed to be) and "There is no preferred inertial frame of reference". and "Inertia is the tendency of an object to resist any attempt to change its motion." (Serway + Faughn College Physics) Okay now I feel ready to cook something up, without taking anyones side here, yet. I'll work up from basics because I believe its the best way to resolve the situation so there are no misunderstandings. In physics, everything is relative to something. Time, length, mass, are all simply relative measures. So is velocity. I stand by the road and watch a car zoom by and relative to me its moving, but relative to the car its stationary and I'm the one thats moving. Time is relative to velocity. This has been proven with experiments which show differences between times on atomic clocks which have been moved at different velocities, one stationary (relative to the earth) and one moving (relative to the earth). Now, i have to clear up what an inertial frame is. Please correct me if I'm wrong. I'm standing on a train moving at a constant velocity and I throw a ball directly up in the air. To me, the ball travels up and down and lands straight back in my hand. To someone standing outside the train looking in they see the ball travel up out of my hand, following a parabola and landing back in my hand. Both observers saw the ball obey the laws of physics (gravity), and since "All laws of physics are the same in all inertial frames", both observers were in an inertial frame. In inertial frame simply describes any situation where all observers confirm the laws of physics have been obeyed. Now, I've just caught the ball in my hand, and I decide to throw it straight up in the air again. A few moments later, the driver slams on the brakes and an acceleration occurs. I manage to hold myself still as I watch the ball suddenly "accelerate" with no apparent force applied toward the front of my carriage and bounce off the wall in front of me. A person standing outside the train would have seen the ball travel in an arc and then bounce off the front of the carriage. The person outside the train saw the ball obey the laws of physics. But me, inside the carriage, I saw the ball suddenly shoot off forwards without any apparent force being applied, which apparently defies the laws of physics. This would lead me to immediately assume that the laws of physics have been broken, and therefore Acceleration does not count as an inertial frame of reference, since "All laws of physics are the same in all inertial frames", and if a law seems to be broken, then heck its not an inertial frame anymore. So, given the initial spaceship scenario, modified for simplicity: Ship (A) takes off from point B in space and accelerates for a time, reaches a velocity, accelerates again (turning around), and returns to point A once more. If you believe, like modern physics does, that acceleration does not count as an inertial frame, then An observer at A (relative to B) is not in a valid inertial frame of reference when undergoing relative acceleration. An observer at B (relative to A) is not in a valid inertial frame of reference when undergoing relative acceleration. Relativity is preserved only when there is no relative acceleration. Otherwise relativity fails. It seems illogical that relativity should fail at all. (back in the train) However, upon consideration as an observer inside the train, I am able to measure (using the right instrument) the absolute force of negative acceleration applied when the driver slammed on the brakes, and using this observation I can explain the apparent sudden acceleration of the ball, and using physics I can calculate its trajectory, so it hasn't in actual fact broken any laws of physics to any observer. Acceleration is still an inertial frame of reference. so, (back in space) An observer at A (relative to B) is always in a valid inertial frame of reference. An observer at B (relative to A) is always in a valid inertial frame of reference. Relativity is preserved even with relative accelerations between A and B. So, one thing needs to be resolved before we can calculate the differences in ages. What is an inertial frame of reference? It seems to me like theres a piece of circular logic in physics, but It may just be me, can someone explain this better... I understand that inertia is the tendency for an object of matter resisting a change in its state of motion. But how does acceleration cancel out inertia??? Even if you are applying a force (acceleration) to an object you still have to oppose its inertia (mass and velocity). Even though you are accelerating it, its inertia will still oppose this acceleration. So if inertia is always there (in the form of momentum), how can acceleration invalidate an inertial frame of reference? Thanks for reading this its been great to exercise my brain on such a fundamental basis of physics. Put maths aside for a moment, forget the formulas for a while, and using logic try to explain how acceleration cancels inertia thus invalidating an inertial frame of reference. Thanks.
Re: My spin One in which Newton's laws hold. Equivalently stated, one that experiences no outside forces and is following a geodesic in spacetime. What? Inertia is not momentum. Inertia is the quality of matter embodied by Newton's second law -- if you apply no forces, there is no acceleration, and the body moves in uniform linear motion. - Warren
Sorry I should have been more specific with the "how does acceleration cancel inertia" Its 7:51 am here and I've been up all night reading this stuff so maybe I'll go to sleep, think about it a bit and come back Please Register or Log in to view the hidden image! But first, I quote from my text (newtons first law btw): "The resistance of an object to a change in its state of motion is called inertia" Okay, bear with me here. Inertia is the resistance to change in state of motion. When you apply a force (acceleration/change in motion/whatever) to an object, does it stop resisting the change in state of motion? Does inertia cease to have an effect? If it does, or if theres some other law that I've missed, then I need to find out why and study it. If the object continues to resist the change in its motion (due to applied force), then is that inertia? If inertia is still present when a force (acceleration) is applied, then I can't grasp how acceleration invalidates the inertial frame of reference. What you would have is some sort of accelerating frame of reference, or some such thing. Relative to the acceleration, the object has inertia.
No. When you hit a tennis ball with a tennis racket, the ball pushes on the racket just as much as the racket pushes on the ball. The ball resists the change in motion by pushing back on the racket. This is inertia. If the ball didn't resist accelerating, then just the slightest nudge would accelerate it to light speed. It wouldn't require any energy to make anything move. - Warren
Neither do I Please Register or Log in to view the hidden image! Alright, so the laws of mechanics are the same in all inertial frames of reference. If a force is applied to an object, is generally understood to ... intefere with inertia in some way? Thats what I don't get. How come acceleration breaks newtons law of inertia? No where in his law have I seen anything that says this is the case. Exact wording Newtons first law of motion, the law of inertia "An object that remains at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, constant speed in a straight line), unless it experiences a net external force" So I must assume the oppisite is true as well "If a net external force is applied to an object that is at rest, then it will no longer remain at rest. If a net external force is applied to an object which is in motion with constant velocity (constant speed, straight line), then this velocity will be changed (change of speed and or direction)" It still doesn't say "If a net external force is applied to an object then it no longer has inertia" So how does acceleration stuff up an inertial frame of reference?
I think I see what Hoodlum is looking for. "Inertia" is, as chroot said, that property of material bodies which reisists acceleration. An "inertial reference frame" is a reference frame that is not accelerating. So... An accelerated frame is non-inertial by definition. That does not imply that anything is 'done' to the inertia of the body attached to the frame (if there is one). Tom
You have to realise that the words "inertia" and "inertial reference frame" mean different things. Roughly speaking, inertia is equivalent to mass. For a given force F, the acceleration of an object is given by a = F/m, where m is the mass. The bigger the m, the smaller the a for a given force. So, the bigger m is, the more resistance the object has to being accelerated. Inertia is just another term for this resistance to acceleration. An inertial reference frame is one in which Newton's laws (such as F=ma) apply without the need to introduce forces with no apparent cause - so called "imaginary" or "inertial" forces.
hmm... ponderous Please Register or Log in to view the hidden image! as a side note general relativity states "all the laws of nature have the same form for observers in any frame of reference, whether accelerated or not"... Thats telling me. I think I need more of an explaination sorry. Now I quote from my book: "Inertial frames of reference are those reference frames in which Newton's first law, the law of inertia, is valid." If you want to take things by definition, then taking the definition of the law of inertia you will find inertia exists despite the forces acting on it. The law of inertia explains what happens when forces are applied to an object, and what an object does when it has no force applied to it. It doesn't say that an acceleration is un-inertial. Do I have to throw aside logic in this case and just believe? By definition, acceleration is simply the change in velocity of an object over time. It implys nothing about inertia, other than the fact that a force must be applied to the object, which depending on the mass (inertia) will produce acceleration. An accelerating object is still trying to be in its previous state (inertia), such as pushing a shopping trolley around it is the acceleration force which keeps it going and the inertia which opposes the acceleration. If an object is accelerated its inertia remains the same, only its velocity has changed. Wheres Einstein when you need a good explaination of a theory. You have managed to inform me that you believe: An "inertial reference frame" is a reference frame that is not accelerating. and its exact opposite An accelerated frame is non-inertial by definition But you haven't said WHY?
How about you go back and read my explainations behind my reasoning? I thought I made it perfectly clear that I know exactly what inertia is, and exactly what an inertial reference frame is as defined in my trusty books-o-physics. The thing is, and this is where my problem lies... The definition for inertial reference frames, along with the definition for inertia, doesn't even hint at acceleration breaking the law of inertia. Let me restate, to save you from having to scroll up a few topics: Can you see why I would believe that applying an external force to an object does not violate newtons first law? Read the law carefully, try to put yourself in my shoes as a person trying hard to see why his understanding is so different. Tell me which part of the law states that acceleration violates the law, because if what you are saying is actual truth (not just popular truth) then the paradox makes sense. Because understanding whether or not acceleration violates newtons law of inertia is parmount to understanding the meaning of: "All laws of physics are the same in all inertial frames" What I'm after isn't further definitions of the laws, or even some maths to describe more accurately the relationship between them, but thanks anyway. I would like to know how you personaly made the leap in understanding, what gap is missing in my logic that you seem to have filled so easily in your own? Can you please explain to me in detail the understanding you have of this law? What makes you think acceleration and inertia are mutually exclusive? Don't say "by definition" again because if you read the definitions you will find that they say nothing that you seem to believe they do... Unless my definitions are flawed?
Hoodlum: There is no "why". The term "inertial reference frame" is <b>defined</b> in a particular way. That definition turns out to be useful because we can say certain things about the laws of physics in inertial reference frames. <i>If you want to take things by definition, then taking the definition of the law of inertia you will find inertia exists despite the forces acting on it.</i> For "inertia", read "mass", and this is pretty self-evident. <i>By definition, acceleration is simply the change in velocity of an object over time. It implys nothing about inertia, other than the fact that a force must be applied to the object, which depending on the mass (inertia) will produce acceleration.</i> F=ma, so inertia and acceleration are related, as I explained. <i>An accelerating object is still trying to be in its previous state (inertia), such as pushing a shopping trolley around it is the acceleration force which keeps it going and the inertia which opposes the acceleration.</i> No force "keeps it going". The pushing force and the friction which opposes the push are equal when the trolley is moving at constant speed. <i>If an object is accelerated its inertia remains the same, only its velocity has changed.</i> Again, substitute "mass" for "inertia" and it's obvious. <i>"An object that remains at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, constant speed in a straight line), unless it experiences a net external force"</i> Correct - Newton's first law. <i>So I must assume the oppisite is true as well "If a net external force is applied to an object that is at rest, then it will no longer remain at rest. If a net external force is applied to an object which is in motion with constant velocity (constant speed, straight line), then this velocity will be changed (change of speed and or direction)"</i> Also true. <i>It still doesn't say "If a net external force is applied to an object then it no longer has inertia"</i> Right. Force doesn't affect mass. <i>Can you see why I would believe that applying an external force to an object does not violate newtons first law?</i> Yes, and you're right. It doesn't. <i>What makes you think acceleration and inertia are mutually exclusive?</i> Nothing. I've said that they are mutually interdependent. F=ma.
James thanks for this btw... Can you read my last post, I posted it just before your reply to my last one.
What I'm after isn't further definitions of the laws, or even some maths to describe more accurately the relationship between them, but thanks anyway. I would like to know how you personaly made the leap in understanding, what gap is missing in my logic that you seem to have filled so easily in your own? Can you please explain to me in detail the understanding you have of this law? What makes you think acceleration and inertial frames are mutually exclusive? Don't say "by definition" again because if you read the definitions you will find that they say nothing that you seem to believe they do... Unless my definitions (or understanding of them) are flawed?
Hoodlum: It seems to come down to this: <i>What makes you think acceleration and inertial frames are mutually exclusive?</i> In a non-inertial frame of reference, "inertial" forces will always be seen. Those forces apparently have no source. For example, consider a rocket in free space, either stationary or travelling at constant velocity. A tennis ball will float in place inside the cabin. A person watching it would say it has no net force on it, so it doesn't accelerate. Now, accelerate the rocket. Suddenly, the ball starts moving, from the point of view of somebody inside the rocket. But that person perceives no new forces on the ball. They still say there is no net force, but they observe an acceleration. The only explanation which makes Newton's second law continue to work in the accelerating rocket is to introduce an "imaginary" force which makes the ball accelerate. These imaginary forces exist in all non-inertial reference frames. As a rule of thumb, it is fair to say that an accelerating frame is non-inertial. As a rider to this, however, you have to bear in mind that free-fall in a gravitational field is not an accelerating frame according to Einstein's theory of general relativity. Now, without bringing gravity into it, can you think of any accelerated frame of reference which would be inertial? I can't.
Okay this is definately what it comes down to, and I can see two sides to this: The person inside the spaceship is able to physically feel the force of acceleration upon themselves. They can also measure the change in motion (acceleration)using fairly basic instruments (masses on springs at the least). The only physical explaination for a change in motion is acceleration. If a force is measured (or felt) an acceleration must have occured. Theres no other physical explaination for a change in motion. So, what about the imaginary forces? If you are in a spaceship (in zero gravity) and you place a ball in front of your head so that it floats perfectly still (relative to the ship), then you accelerate, the ball will hit you in the face thanks to the law of inertia. What you saw was the ball accelerating toward your face, however, if you have two acceleration measuring devices (accelerometers?), one on the ball and one on the ship, then you will measure a change in motion on behalf of the ship, and not the ball. The ball will keep its initial velocity until it bounces off your face. So the obvious conclusion is that the ship changed motion, not the ball, even though relative to the inside of the ship the ball "appears" to the naked eye to move, the ball will "appear" to the "accelerometer" NOT to move. There is no "imaginary" force, because the velocity of the ship can be measured to change, and the inertia of the ball can be measured not to change, despite all appearences to the contrary. So: If an object in your frame of inertial reference breaks the law of inertia, your frame of inertial reference has been accelerated. Meaning the inside of the spaceship still looks the same, but the ball just accelerated itself "apparently" breaking the law of inertia. What really happened is the ship itself moved, and the ball kept going on its original journey (for a while at least). Not so, to my understanding. Whenever you see an "imaginary force" the only explaination is a change in the movement of you inertial reference frame. In my understanding accelerating an inertial reference frame is okay, because acceleration still complys with the law of inertia, which is the condition that the inertial reference frames are based upon.
