This is commonplace in introductory physics. We presume “perfectly” elastic collisions, as if particles were infinitely dense, and as if the surface of the “ice” were perfectly frictionless.
This is why I allowed the hockey player to skate up alongside the moving puck, matching velocity with it. Then, when he swings his stick, it moves 10Kph faster than he is moving, then adding 10Kph to the puck’s speed.
Nope. Wrong. It works for the “ideal” model, where momentum and energy are transferred with no loss.
Actually, it works the other way around. The compression of the beach ball causes a significant loss of momentum and energy, and the beach ball moves more slowly than it would if it were fully inflated. Go out and hit a half-filled beach ball, and then a fully inflated beach ball. Bat them around for a while, and you will see.
This, for once in this entire thread, is an experiment you can actually perform for yourself, in your back yard, at almost no cost.
(Comparably, try playing billiards with dough balls or balls of modeling clay.)
Huh? It’s a central and direct consequence of special relativity! If you plan to revoke SR, then it is without explanation, so your theory ought to offer an alternative – if it doesn’t, it’s simply inadequate.
I like how that paper supports the assertion that the ether has a mass through appealing to special relativity…
Which just adds one more refraction – again, the star will move at different speeds relatively to the interstellar ether, so the light must either be sped up or slowed down, leading to different angles of refraction.
Where it is, depending on the Earth’s movement relative to the interstellar ether, refracted again.
But the speed of light coming from the sun never changes its velocity, and is thus only refracted through a constant angle. Think of a really hot day, where the medium (air) changes its refractive index: the observed blurr is just what I’m describing. Remember, refraction occurs because the light has a different speed in different media, so any change of the speed of light must lead to different refractions.
True, but that ether itself moved with respect to, say, the interstellar ether, or the Earth’s ether.
That’s not necessary, and I’m not even sure it’s true – you have to expend quite a lot of energy in order to get anything to space. In any case, if your theory only holds for rockets that fulfill this requirement, then it’s obviously not very general, indeed, can be reduced to the tautology ‘everything that moves slower than its push force, moves slower than its push force’. Special relativity needs no such proviso to explain the motion of rockets.
This is exactly the same thing I said, only with the roles of exhaust and rocket (mass-wise) reversed, so if I was being silly, then you are, too.
In any case, the assertion under discussion was that nothing can go faster than its push force; which is wrong even in your example, since the exhaust is pushed by the rocket, and goes faster than it. So that statement is simply completely meaningless.
In which case, you get the notion of ‘elastic collision’, precisely the one used in the wiki example, which, I might add, is an elementary textbook Newtonian mechanics problem.
This violates conservation of energy. Each ‘re-forming’ can only give back the energy expended in the compression, thus yielding as a maximum the case of elastic collision, where all energy is conserved; if, as is typically the case, energy is carried off into other degrees of freedom (the sound you hear as the puck is hit, heat, etc.), the collision is partly inelastic, and the puck will end up travelling slower than the possible maximum.
SRT is used to ensure every observer sees the speed of light as c. If, as is usually the case, the observer is stationary WRT the aether (or very nearly stationary), and c is WRT the aether, then the observer sees the speed of light as c anyway, with no recourse to Lorentz equations. So aether or SRT makes no difference to e = m / c^2.
I missed that, so please show me where it is. And I like how the relativistic explanation of the Sagnac experiment uses an arbitrary reference frame ie the aether.
The light coming from the sun does change its velocity, but that does not automatically mean a refraction. If the light is at the normal to the (eg) glass, it changes velocity but is not refracted. If it is not normal to the glass it is refracted twice, to leave the glass at its original velocity and angle. The velocity in space is c, in our atmosphere it is c/n(air), coming in through our window it is c/n(glass). If the window is double glazed, repeat.
For a start the rocket is more massive than the exhaust, not the other way round.
Look at the exhaust at the base of the rocket on the launch pad, it is leaving the nozzle at a speed of a few hundred Kph. It escapes down the flame tunnel and out into the open in second or so – a distance of a hundred meters or more – and that is just the exhaust that you can see. In that time the rocket rises a meter or so. Which is more massive? We have also discussed hockey sticks and pucks, snowballs being thrown etc, so we are talking generally.
I said to use the correct reference frames and quantify correctly which you did not do. The speed of the rocket can never exceed its exhaust speed between the active FRs. The active FRs are remember FRR, and FREn. If you break the action/reaction down into separate FRs and deal with them individually as I have done you will see that.
So, no this is not what I said. Read it again. The rocket is 10 tons, the exhaust is 1ton. The exhaust speeds off at 550 Kph WRT the rocket. According to an observer in an arbitrary FR which was stationary relative to the rocket before ignition, the exhaust speeds off at 500 Kph, and the rocket speeds off at 50 Kph in the opposite direction. This means that the momentum of the exhaust is 500 X 1 = 500 : the momentum of the rocket is 10 X 50 = 500. Momentum conserved.
Nowhere in that statement does the rocket exceed the speed of the exhaust. If it is turned round as you stated, with the exhaust more massive than the rocket, the rocket and exhaust change places, with the rocket at 500 Kph. It still does not exceed the speed of the exhaust. That is why I said you were being silly. You are also possibly nit-picking over the fact that I did not explicitly state that there were only two FRs involved. I did that in the original example. When we move on to the next reference frame, which is FRE1, the rocket (your rocket which is less massive than the exhaust) will be at 1000 Kph relative to the arbitrary FR, but will still be at only 550 Kph relative to FRE1, which is now the exhaust. The rocket can never be faster than 550 Kph relative to the active FR.
If you read my posts, you will see I break down the reference frames for ease of understanding into small time slices. These are called FREn and act/react one at a time with FRR. The action/reaction is between two frames and two frames only, and the time slices can be as small as you want. These are the active frames, and cannot move apart any faster than 550 Kph in the above example. Relative to FREn, FRR cannot exceed 550 Kph.
The rocket can never exceed the speed of the exhaust between the two active frames. I have gone over this time and time again. what is so difficult to understand? That question is a quote from this forum directed at me by the way, do not blame me for it.
My statement about compression effects was based on observation and common sense. Hit a balloon which has no horizontal movement with your hand. The balloon deforms and then reforms, so leaving your hand faster than the speed of your hand through the air. Of course it slows down again very quickly due to air resistance.
If a ball is struck by a bat which is being swung at 10 Kph relative to the ground (assume linearly), and it is non elastic it moves off at 10 Kph. Now assume the ball deforms to half its size along the line of travel as the stick hits it. The stick is still in contact with the ball, and still moving at 10 Kph, but the ball is now half its previous size along that line. The ball then reforms at 5 Kph to its original shape while still in contact with the stick. 5 Kph is 1.4 m/s, so if the ball is 0.5 M diameter it will take about 200 milliseconds to spring back from 0.25 M to its original 0.5 M size. At that point it leaves the stick with a speed of 15 Kph relative to the ground. To allow for “energy is carried off into other degrees of freedom” deduct the appropriate speed.
If the speed of light wasn’t absolutely constant, but only locally constant, we should be able to measure differences in the timing of the orbits of moons and planets, smaller than, but similar to the measurements done by Ole Rømer in 1676 used to establish a speed of light.
If a balloon is dropped (in a vacuum) from height x, so that it reaches 10Kph on reaching the surface, it will rebound with a speed of 15Kph in the opposite direction. This means that the maximum height the ball will reach is now 1.5x, and upon falling back to the ground will hit with a speed of (obviously) 15Kph.
But that now means it will bounce with a speed of 22.5Kph, reach 2.25x, hit the ground again at 22.5Kph… :smack:
Congratulations you have just acheived (better than) perpetual motion.
No. The derivation of the formula depends on the Lorentz transformations, so if those didn’t hold, E = mc[sup]2[/sup] wouldn’t, either.
Ref. 10 is Einstein’s ‘Does the inertia of a body depend upon its energy-content?’, i.e. the E = mc[sup]2[/sup] paper.
I don’t think that this is used in any essential way in the paper, though; rather, what the author does is just to introduce another ad-hoc hypothesis (another speed for light to propagate at in matter) to produce agreement with experiment, which of course one can always do; but this is vacuous and trivial. Any experimental data can be incorporated in this way, simply by elevating it to the status of an assumption. The strength of relativity is that beyond its two axioms, it doesn’t need any others to explain a wealth of data.
It doesn’t.
But we’re not at the center of the Earth (and thus, the center of the Earth’s gravitational field), so the light that reaches us is not normal to the boundary between the ‘interstellar ether’ and Earth’s ether/gravitational field or what have you.
But we’re in the Earth’s gravitational field, i.e. in the glass, in this example; we don’t look at space through it. So, since the speed of the light impinging on the ‘glass’ changes, because the speed of the movement of the binary with respect to the Earth changes, the angle of refraction changes.
That statement just says ‘the difference between the speed of the rocket and the speed of the exhaust is never greater than the difference between the speed of the rocket and the speed of the exhaust’, which is as obviously true as it is vacuous.
But let’s not muddy the waters here. Your claim was that particle accelerators and such don’t accelerate particle’s beyond the speed of light, because ‘nothing can exceed the speed of its push force’. I have given you explicit examples – the stationary electric field, the exhaust that’s heavier than the rocket, the jet being accelerated via a ground-based engine using a mass greater than that of the jet – where this does not hold. And nevertheless, particles in particle accelerators don’t exceed c, and neither will your rocket, even though it has an ‘internal motor’. It is simply the relativistic kinetic energy – which I might add is what implies the mass-energy equivalence above – diverging at v = c that makes such a thing impossible.
Which is a very good demonstration for how common sense can mislead you, even on relatively simple matters such as Newtonian mechanics, to say nothing of special relativity. And in this case, as BunnyTVS above demonstrates, you could actually have used your intuition to get the right answer, which is not the case in SR.
I have said again and again that that statement is between active FRs, and only active FRs. Your statement “the jet being accelerated via a ground-based engine using a mass greater than that of the jet… [can travel faster than the speed of the exhaust]” is simply fatuous. You cannot pretend to be discussing in good faith while you trot out nonsense like this. I cannot carry on pretending that you are simply mis-understanding me. You know full well that I am correct in saying that nothing can exceed the push force between the active frames , but you just cannot make yourself admit it. In agreeing with BunnyTVS, you are showing a remarkable lack of judgement. See my answer to him.
On your assertion that an arbitrary FR (ie aether) is not used to explain the Sagnac effect, here is a part description from R Ortvay (no particular reason for picking him, he was just the first on the google list)
“However, Sagnac’s experiment can be interpreted exactly by general relativity, when we, like in the treatment of the centrifugal forces[5], relate the line element to a coordinate system that rotates against the system of fixed stars.”
If the speed of light is c to all observers (and therefore receptors), why is he using a coordinate system that is not only external to the experiment, but external to the Earth? This reference to another FR is in all relativity explanations, and what is it if it is not the aether?
The reason you appear to get stupid replies is because we appear to be getting stupid hypotheticals.
Nowhere in that post do you mention both the bat and ball in motion. That however is irrelevant. The individual speed of the objects is of no consequence in the above case. All that matters is the difference in speed between the two. And I bolded that sentence to avoid your obvious follow up that “Are you saying there’s no difference between two objects moving at 10Kph, and two moving at 1000Kph. I can tell that’s false just from common sense.”
So floor up 5Kph and ball down 5Kph == Floor up 10kph and ball stationary == Floor stationary and ball down 10Kph.
Really, it’s just elementary Newtonian mechanics. I’ve already linked you to the example on wiki. As you can see, the second cart speeds off at a speed about twice that of the first one, i.e. of the ‘push force’.
Any statement in relativity is only meaningful if the reference frame in which it holds is given. The fixed stars is merely a convenient way to specify an (inertial) one; a frame at rest with respect to Earth is never perfectly inertial, because of the Earth’s orbit and rotation, and the ‘fixed stars’ are simply an unambiguous description of an inertial frame. If you look to wiki, it’s explicitly explained that
So your explanation could appeal to any other frame equally well.
“All that matters is the difference in speed between the two” is usually (but not always) correct. The difference in speed between the two is :- bat 10 Kph towards the ball: ball (or to be precise half a ball) as it springs back into shape 5 Kph towards the bat: total 15 Kph. We are in agreement there. It therefore leaves the bat at 15 Kph, exactly in accordance with your last sentence above - why are we arguing?
The reason I put “not always” in there is because there are occasions when it is just not true. There may be no relative speed difference between bat and ball but the ball moves off at 10 Kph relative to the ground. I have already mentioned this, but a refresher seems to be in order. The bat is stationary relative to the ground, the ball is in contact with the bat, and is therefore also stationary relative to bat and ground. The bat starts to move along the imaginary line connecting it to the ball until it reaches 10 Kph WRT the ground when it stops. The ball is obviously moved by the bat and is accelerated to exactly the same speed as the bat ie 10 Kph relative to the ground. When the bat stops the ball does not. Newton’s first law. Note that there was never a difference in speed between the two.
This is what you put in your previous post.
“So what are are saying is…
If a balloon is dropped (in a vacuum) from height x, so that it reaches 10Kph on reaching the surface, it will rebound with a speed of 15Kph in the opposite direction.”
That is not what I said. If it is a deliberate mis-quote I stand by my statement that it is a stupid reply. If you mis-read what I said, perhaps it was only a hasty reply.
As I said last time, this is a load of bunkum. Nowhere is elasticity mentioned. The formula given does not mention mass or elasticity. It is meaningless.
There are two frames used in SRT, the transmitter and the receiver. The speed of light is the same for all observers (receivers). All other frames are irrelevant for working out the speed between transmitter and receiver which is by SR’s definition c. As there is no relative motion between Tx and Rx, the two light beams should arrive at the receiver at the same time no matter which direction they are going round the rotating path. They do not. If you use a third FR, and relate the speed of light to that, that FR becomes the aether. Please explain the Sagnac effect without recourse to a third reference frame. You are of course allowed to say that WRT this arbitrary frame, the Sagnac Interferometer is rotating. What you are not allowed to do is to refer the speed of light in the interferometer to this FR. The light is generated and transmitted in the interferometer, and is received in it also. It never goes outside it.
No we are not in agreement. Classical physics says you are wrong. The maximum theoretical velocity in an elastic collisionis based purely on the momentum of the two objects.
But it seems you want it both ways.
I don’t know if you need this is large red font or not but…
This is exactly the same as the first hypothetical :smack:
It doesn’t matter if either object was moving prior to contact or if you start moving the bat with the ball next to it. As soon as you start moving the bat you are altering it’s momentum. And the transfer of energy in a collision is all about the momentum between the two objects.
You appear completely unable to distinguish between theoretical models and real world situations. For example a perfectly elastic body in physics does not deform. That’s why in the real world we use balls as rigid as possible for most sports, we get the maximum possible conservation of momentum.
There are lots of real-world examples of reactions that are greater than the speed of the force that causes them.
A bowling pin flies away from the bowling ball much faster than the ball was travelling.
A golf ball flies away from the driver much faster than the driver was moving.
(This one is a bit tough, because golf club manufacturers do account for various “springy” effects, such as a flexible shaft, etc.) But…substitute an aluminum baseball bat for the golf club: the ball will fly away much faster than the bat was moving!
One of my favorite experiments – and anyone can do this at home! Get a basketball, a soccer ball, and a golf ball. Hold them, one above the other, vertically, with the basketball lowest and the golf ball uppermost. Drop them all at once. The basketball hits the floor and bounces up. It causes the soccer ball to bounce upward faster, and this, in turn, causes the golf ball to fly upward really fast! I’ve seen the golf ball fly thirty feet into the air. Much fun!
I missed this the first time I read it. Thanks to you BunnyTVS for drawing my attention to this. Look again at the Wiki carts page below.
]File:Collisioncartsm1greatergreaterthanm2.gif - Wikipedia
Turn the diagram anti- clockwise 90 degrees, make the cart on the left the size and mass of the Earth (or just go find a place on Earth which approximates the material used in the cart. Drop a much smaller mass of the same material used in the cart, and it will bounce faster and go higher than the height you dropped it from. It will then fall back and bounce faster and higher still, untill eventually it reaches escape velocity and does not fall back.
