Hi zion, Allow me to quote (Q)'s post from a few days back: So the formula for M you gave is completely equivalent with the energy formulation: an infinite amount of energy is required, there is no such thing as adding an infinite amount of energy to an object, hence the vehicle will never reach the speed of light (it will approach the speed of light more and more though). The reason I repeated that M does not stand for restmass is simply because often people reason that you actually gain restmass when accelerating, while this is ofcourse not true. Anyway, that is the answer Special Relativity gives us. One is ofcourse free to believe it or not Please Register or Log in to view the hidden image!. Bye! Crisp
I'm not sure that I understand Crisp either. I don't see what the atomic energy inside the object has to do with it's potential maximum speed (not to be confused with velocity...we are talking speed here?) Gravity does not increase the potential energies of an object, just changes them from one to another. So if you have an infinitly high slope in an infinite gravity field then the Ep is infinite. As the object moves down the slope, Ep changes to Ek eventually giving infinite Ek and so infinite speed.
But how does an infinite amount change to 0? Infinite means "has no end", how can a value with no end reach 0? Where do we draw the line, where does the Ep change to 0? As you can see, infinities bring up all sorts of problems, and the only way to solve this question is by using infinities. Im a firm believer in the idea that infinities in any equation mean we have either done something wrong, or the equation cannot be applied to that problem. Also, if we have an infinite Ep, a finite Ek and an infinite time period in which the object could potentially reach c, it's obvious it will not. It's not as easy as dividing out infinitiy/infinity=1. If it's there for an infinite amount of time, it will never reach c because Ek will never reach infinity. Am I coming across ok here?
Infinities are often defined in terms of limits of infinite sequences. Dividing one infinity by another infinity implies dividing the terms of the first sequence by the terms in the second and then looking at the limit. The limit might turn out to be infinity, zero, or any other number depending on the sequences involved. (Or the limit might not exist. The “limit” value might not “settle” on any value.) Some of the “mathematical” tricks in physics aren’t formally correct. They work only because of additional properties of the universe that are seldom formally stated. (The average physicist would have to spend too much effort studying arcane math to understand those other properties. And for what purpose? All the systems the physicist looks at have those properties. Why should the physicist care about the weird spaces that don’t have those properties?) Physicist: “So is my answer correct?” Mathematician: “Well…yes. But only because…” Physicist: “Whatever.”
Attempted clarification Hi all, Esp, "I don't see what the atomic energy inside the object has to do with it's potential maximum speed (not to be confused with velocity...we are talking speed here?)" Sorry, in my native language there is no difference between "speed" and "velocity", that probably gives rise to some confusion as I mix the terms. I'm talking speed ofcourse (the size of the velocity vector). Now, even a macroscopic object has energylevels just like an atom does. A collection of atoms has different energylevels than the individual atoms, but is has an energyspectrum nevertheless. However, that is not really relevant for the discussion: in Newtonian and Relativistic mechanics, energy is associated to an entire object, and is not immediatelly related to energylevels of the constituting atoms. Both Newtonian and Relativistic mechanics have no upper limit to the energy a massive object can have. The major difference between the two is the limitation of speed Relativistic mechanics has (and we know from experiments that Relativistic mechanics from the Special theory of Relativity is closer to reality than Newtonian mechanics). Xelios, "But how does an infinite amount change to 0? Infinite means "has no end", how can a value with no end reach 0? Where do we draw the line, where does the Ep change to 0?" Potential energy is always relative to a chosen energylevel. Most of the times the value Ep = 0 is associated at infinity. However, we don't need that either for the reasoning: - As we all (seem to) agree on, an infinite slope with no friction, ... has the possibility to push the kinetic energy of the object (which in relativistic mechanics is actually the only "real energy", i.e. observable). As the object falls/glides down the slope, it gains more and more energy because it is contineously accelerating. - This (kinetic) energy increases every second, but it will never get infinitely large (= the energy needed to gain lightspeed). It doesn't matter how long we wait, the energy will never reach the value "infinity"... It will get very large, but since we add a finite amount of kinetic energy every second, it takes an infinite amount of seconds to get an infinite amount of energy. Imahamster2, "Some of the “mathematical” tricks in physics aren’t formally correct. " I think this is formulated in an unfortunate way: I'd personally say: "some of the mathematical tricks in physics aren't formally proven yet, but by experiment have been proven to work in the scenarios we can think up at the moment" Please Register or Log in to view the hidden image!. Also, there's nothing in the reasoning stated above that needs some dirty non-mathematical trick to work, it can be proven very nicely. Bye! Crisp
If we take another look at Mcloud]/b] thought experiment, we know that the cart is moving down a frictionless slope. In other words, the cart is not powering itself. It is relying on a gravitational source. Therefore for the purpose of the thought experiment, we can remove the slope altogether and imagine the cart freefalling towards a source of gravity. The source must be massive enough to pull the cart towards it in order to reach near light speed. Does this sound familiar? Essentially we are talking about an object accelerating towards something massive, a black hole for example.
well I havent read the entire thread due to laziness, but I thought I'd mention that if space could be folded then it would be possible to exceed the speed of light, but only relative to the outside because the actual object would still have mass....blah blah...blah.... and if you were in space, why would you want a frictionless surface to travel on? and I think that if this frictionless incline plane where on a large enough body, like, oh, say a black hole, then maybe.......... well all I'm saying is there probably is an exeption even though I'm to lazy to chekc em all out right. I'll be back with an ideaPlease Register or Log in to view the hidden image! soon..........
Crisp, didn’t mean to imply you made any math “errors”. Was just remembering with amusement early hamster exposure to some mathematics in physics books where terms were pulled inside and outside integrals and re-ordered with no apparent concern for whether the operations were valid. They were valid but a physics student learning mathematics from those examples might believe such operations were always valid. Understanding the mathematical reason why those operations were valid was beyond the math level of the target audience of the physics book. Certainly the theoretical physicists who derive mathematical physics do understand the math far better than any hamster.
Since this can't happen... why bother worring about it?... Please Register or Log in to view the hidden image! Interesting question though... Please Register or Log in to view the hidden image! Well... if the cart goes on forever, and it accelerates... it most likely will get to the speed of light, unless there is a limit for an actual speed... what I don't think so... We can sucessfully accelarate a particle only until 99.99999...% of the speed of light... Perhaps that's the limit for your cart buddy... Please Register or Log in to view the hidden image! If a little particle can, why not an object? Please Register or Log in to view the hidden image! Love, Nelson
Q has raised a good point Here.Certainly under free fall we would approach velocity of light.true. bye!
