losfomot

I only recently became aware of these lessons, and I'm through the first two... I'll be starting the third after I post this message. I am hoping somewhere in the third there are the answers to the questions in the second lesson. Regardless, this calculus lesson thing is pretty cool, I'm in, and I hope Dave is convinced that there are enough people to keep going soon.

What about in the following scenario: Where > and < depict acceleration... and each # depicts one year of coasting with no acceleration. We have a pair of twins in Spaceships - A and B They are starting at rest wrt Earth. A - >>>>><<<<<<<<<<>>>>> B - >>>>>#####<<<<<<<<<<#####>>>>> So both A and B undergo the exact same amount of acceleration which results in their return to the rest frame of Earth. We'll say that >>>>> is equal to an acceleration that brings a ship to a velocity of 0.5c wrt Earth. So B has coasted at this speed (150,000 km/s) for 10 years longer than A (Because A didn't coast at all, he just turned around immediately when he reached this velocity) So using the formula: T1 = T0/SqRt[1-(v^2/c^2)] B will be about 1.55 years younger than A when they are together again... even though they both underwent exactly the same amount of acceleration. Or do I have this wrong?

Yes, it's stored in the archives of a secret temple in the delta quadrant of the Andromeda galaxy. I can't be any more specific than that because, well, as I said, it's a secret.

Again, it's your terminology. The term 'being instantaneously updated' implies (or, rather, could imply) that someone or something has knowledge or information that is being updated instantaneously. This is not the case. Yes, if the target or source is moving, the instantaneous distance between them is constantly changing. Because information can not travel FTL, you cannot know the instantaneous distance instantaneously.

Right. Not necessarily knowable. Someone may not have the means to measure said distance. The distance still exists though. I feel like a trap is being set. sure. I would change 'being instantaneously updated' to 'constantly changing' and then tentatively agree.

established and maintained? Why would the distance need to be established and maintained in order to be real? Interaction? why? The distance is there, and has a definite value. If you want to know what that value is then go ahead and measure it. You are not going to get an instantaneous value, but you will still get a definite value. If the object is moving it will take a few seperate measurements to figure out how fast and in what direction the object is moving, and then you will even know ahead of time where it will be. If the mirror happens to change its velocity in a random manner, then your pretty much out of luck on successfully predicting how far away it is. However, an inability to measure a distance does not mean that the distance does not have a definite value... (for the umpteenth time) you just don't know what that definite value is. You can call it sound or you can call it vibrations, it comes down to the same thing. You can leave a recorder in the woods and play back the vibrations/sound. Personally, I am sure that plants CAN detect vibrations/sound. It all comes down to what you define the term 'definite value' as meaning. Why don't you rephrase the question without using that term.

O...K.... no, I guess you can't. You will only know for sure in retrospect, after taking the measurement. But this does not mean that the distance does not have a definite value. The only way your original statement could be correct is if you define the term 'definite value' as being any value that you yourself know ahead of time. To define the term in such a way is incorrect (IMO) and a bit egotistical (also IMO) and would obviously lead to your original statement being correct. If a tree fell in the woods, and nobody was there to here it, would it make a sound? Of course it would, just like a distance has a definite value, whether someone has taken the time to measure it or not.

I am going to venture an answer... If the mirror is moving (or could move) relative to you- then even when your pulse of light returns and gives you an answer, it is possible that the mirror has already moved and that answer is no longer valid. I don't think this means it has no definite value though, just an indeterminate value. If the motion was uniform, the distance at any given moment could be worked out mathematically. If you and the mirror are known to be stationary relative to eachother, then it doesn't matter when you perform the measurement, the distance WILL have a definite value... consider that you could perform your measurement, record the answer and then perform the measurement again, and again. Each time the answer will be the same. So you could only wonder about the definite value of the distance the first time you perform the measurement. Every subsequent time you will know the answer before the light pulse returns. You will look back and realize that there is no way you could have gotten a different answer the first time you made the measurement and conclude that the distance DID HAVE a definite value before the light pulse returned... you just didn't know what that value was yet. So, overall, I would say NO, you are not correct in saying that.

I think you are complicating things unnecessarily. You should stick with your original scenario... 2 guns that, when stationary, and side by side, and fired at the same time, release bullets with identical velocities that hit a target at the same time. Now leave one gun where it is (100 yards from target) and put the other gun solidly on a heavy mount on a track that moves the gun toward the target. Set the experiment up so that the moving gun will fire when it is 100 yards from the target. Simultaneously, the stationary gun fires. The moving gun's bullet will hit the target first. velocities are addable (is addable a word?) So if you have a gun that fires bullets at 100 yards per second, and put it on a track that is moving at 30 yards per second in the same direction as you are firing, the final velocity of the bullet, when fired, is 130 yards per second (relative to a stationary target). When the velocities you are dealing with approach the speed of light, you can't just add them anymore, the math gets a little more complicated.

The nature of the universe Nothing can travel faster than c This is not to say that NOTHING is different about the light... The light from a flashlight that is moving toward the target will be blueshifted (have more energy) compared to the light from a flashlight that is stationary (relative to the target) But they will arrive at the target at the same time.

I think the word is 'semantics'. I mean, if you really want to get into details, you could look at the first condition stipulated in this experiment: and conclude that the bullets MUST hit at the same time no matter what they're mounted on.

It's a 1 tonne weight and a coin... If we take air resistance out of it, what do shape and density have to do with it?

I think the 1 tonne weight DOES hit first but only by an immeasurably small amount. For all practical purposes they hit at the same time.

Sorry, poor choice of words. He could use another reference frame... but it complicates things unnecessarily and could lead to mistakes.

He has no choice but to use his own reference frame, in which the other ship is not moving. So he simply points at the other ship and shoots. If he complicates things by trying to look at it from the reference frame of our galaxy, he may decide to shoot ahead of the other ship, in which case he will miss it entirely. You could look at it this way: Why would the captain choose that last star (from which he is moving at 1000 km/s) as a reference point over any other star? If he chose a star in some other galaxy and computed that the ships are moving at 1,234,654 km/s WRT that star, would that help him compute where to fire the laser in order to hit the other ship? No. It wouldn't help him any more than using the closer star as a reference point. It's simply easier to disregard everything else in the universe and focus on whether or not the other ship is moving relative to himself (which it isn't), and then shoot accordingly on that basis alone. by the way, my figure of about 6 seconds in my initial question is wrong, it should be about 3.3 seconds

OK.... Two Spaceships Head out of the solar system... They position themselves exactly 1 million km apart and then accelerate, in the same direction, to a velocity of 1000 km/s. They maintain this velocity until they leave the galaxy (Yes I know this would take a long time). Once out of the galaxy they both coast at this velocity for the duration of my question. So the situation we have is this: 2 ships coasting at 1000 km/s (we'll say relative to the last star they passed while leaving the galaxy) parallel to eachother at a distance from eachother of 1 million km. Oh and they are in intergalactic space (as inertial as it gets). They each have bright lights attached so they can see eachother and they are moving directly towards a distant galaxy (which they will probably never reach at their velocity). Also there is no rotation of any kind. So.. on to my question(s). A - In the race toward the distant galaxy, does each ship see themselves as in the lead? (They are a million km apart and they have a velocity (away from our galaxy), the light takes about 6 seconds to reach the other ship. So each ship should see their counterpart as he was 6 seconds ago rather than as he is 'now'... therefore, each ship should see the other ship as lagging behind about 6000km (1000km/s • 6 seconds)) However... The ships are moving uniformly. They have exactly the same velocity. They are in an inertial frame of reference. B - Are they not at rest WRT eachother? C - If the answer to A and B are both yes, isn't this a contradiction? (ie. When 2 objects are at rest WRT eachother, one can point a laser at the other... shoot... and hit the object. But if A is true, then if one of the ships pointed a laser at the other ship, they would be pointing a laser at the ship's position 6 seconds ago and miss the ship entirely. Of course, this assumption could be the error of my thinking so maybe I'll make that Question # D) D - When 2 objects are considered at rest WRT eachother, can one point a laser at the other... shoot... and hit it no matter how far away it is? (keeping in mind that there is no gravity or any other force acting on the laser, and the shooter is very very good)

Sorry, that's just my 'signature'... I've changed it now... should be less confusing. (edit- my signature was 'there is no gravity... just inertia'... to answer the question, my signature should have (more accurately) said something like : 'Gravity is just inertia' since, of course, there IS gravity.)

I cannot see them either. I am on a mac. I think that as something to do with it.

No, you can't ask a planet to stop moving, but assuming you could, or better yet, assuming you could account for the effect of the motion of all these bodies in your measurement, how do you know that the weight of an object would not vary (or fluctuate) at a precise enough measurement? Is it a definite consequence or law of field theory that gravity is fixed.. even down to planck scales? And what about quantum theories of gravity... with the graviton involved, gravity is still smooth? Still an exact figure no matter how precisely you measure it?

OK... what I was wondering is this... Is it possible that mass (we'll say on the surface of the Earth, for example), at a small enough scale, actually has a kind of brownian motion? And it is only the NET or AVERAGE motion that is seen to be 9.8m/s/s in a downward direction? I believe this would cause slight variations to occur in the sufficiently accurate) measured weight of a (sufficiently small) object. OR If the mechanism of gravity was something akin to gravitons, then each graviton would have its own effect on a small bit of matter. A kind of a tug (let's say). Many gravitons cause many tugs, and together they would create (on OUR much larger scale of matter and time) an apparantly smooth acceleration of 9.8m/s/s If we were to measure an (again, sufficiently small) object accurately enough, shouldn't we be able to detect a 'jerkiness' in it's weight due to the individual gravitons?

I am curious... how accurately have we weighed things? Is there a point where the weight of an object will not stay still? To see this, I imagine, we would have to weigh something in grams to something like 20 decimal places and it would have to be somewhere completely devoid of vibrations. Is there an accuracy point where the weight is no longer fixed... where we would have to calculate the average weight rather than know the exact weight?

If this is true then is there such a thing as truly inertial space (and hence an inertial frame of reference) in the universe we live in? I thought a body was inertial as long as it felt no forces acting on it.