Re: Again, a confusion between relativistic and restmass Crisp, I believe you are right about this, but considering that everything is relative, the restmass of an object compared to one observer would be different from that of an observer who was traveling at a different speed. Or am I interpreting rest mass wrongly? I thought rest mass was considered the mass an observer at same velocity would perceive. Also, I had asked what would happen if I could make an object appear to have no rest mass? Wouldn't it be possible to increase the speed of the object in proportion to the apparent reduction in rest mass? I am not sure (I need to look at Einstein's equations again, it's been a while) but I think a limiting factor would still be the speed of light, although if you could possibly appear to make the object's mass negative (I have no idea of the implications of that Please Register or Log in to view the hidden image!), you could potentially travel at the speed of light for almost no energy. I would definately like to hear your thoughts.
Einstein's special theory of relativity stipulates that the mass of an object increases with its velocity relative to the observer. Thus, when an object is at rest (relative to the observer), it has the usual inertial mass that we are all familiar with (that is,a tendency to resist an applied force) . This is called the "rest mass" of the object. So, quite simply, the "rest mass" of an object is the inertial mass that an object has when it is at rest. Hope this clarifies what is meant by "rest mass" ? A good website for your reference is http://www.bartleby.com/173 .... Enjoy, Henrik
Henrik, Thanks for the link. However, in the context of relativity, what does the word "rest" mean? I take it to mean that it is not in motion relative to the observer, but that does not imply the object is not in motion, only that the observer and the object are synchronized in motion. When you think about this, what does mass really mean then? What is the frame of reference for the definition of "rest"? Only the observer?
How about rest mass relative to the (still theoretical) Higg's field(s) arising from the quantum vacuum? Presumably, it is not (yet??) possible to know if the universe is rotating, or if the quantum vacuum undulates, to know if such reference frame dragging might contribute to ill determinion of absolute rest mass. But maybe a purely speculative, moving mass, Higg's field force doppler shift might allow the determination of an object's least complex possible value for rest mass.
Mr. G ... I've heard of a Higgs field and a Higgs boson ... So when did Higg get in on the act? Although, I must say, it's a reasonably decent act. Thanks for the chuckle Please Register or Log in to view the hidden image!
Not I ... But rather thee ... Jest on! You will defeat them yet! Just remember: Lower the portcullis before the fall of night.
Chagur, Feel free to offer anything of substance to the conversation, anytime. You may start now if you wish. Please Register or Log in to view the hidden image!
OK, so let's assume that we can determine some specific quantity called mass and relate it to the rest mass in reference to the Higg's field arising out of the quantum vacuum. What are the potential effects we could realize if we could somehow shield the mass from the gravitational effects of the universe and the universe from the gravitational effects of the mass? Could we in fact somehow drive an object faster than the speed of light? Also, here is a separate question I have often wondered about. Given an object traveling at the speed of light (assuming it could be brought to that speed), if a force was applied to the object in the direction of velocity, what would happen? Since F=m*a, what would happen to the object?
SeekerOfTruth, Erm....I think the answer to this one is "No". My physics is a bit rusty these days, but I see where you're trying to go. Your object would still have a restmass in your local region of space, and should you attempt to move this object, you will create a new frame of reference, relative to your frame of rest. The laws of physics, and hence relativity, would still apply to your object, thereby imposing the same limit implied by E=mc^2 (anyone able to back me up on this one, or am I talking out of my behind?) Newtonian physics do not apply when moving at relativistic speeds, but anything could happen. "Timetravel" is theoretically possible (reversing the arrow of time) and so too is the possibility that the object can be everywhere in the Universe at the same time.....(at least on a quantum scale). Not only that, but the energy would also have to increase to infinity (and beyond...?) If I'm waffling feel free to rubbish me..... Cheers, Henrik
... The truth and Henrik The law of relativity states that the fastest anything can travel is the speed of light (even the thought should be bound by that condition). An object with no mass (only energy, but energy is mass according to E = MC^2) can only reach the speed of light, hence the light (small energy packets with no mass) travels at the speed of light. If you make a graph of the relativistic time and mass (energy) implications of travelling near speed of light, you will se that however one looks at it, you can get near to the speed of light if the mass is very small (infinite decimal), but you can never reach the speed of light or break it. In conclusion: If the laws of relativity is correct, the only way of traveling between two points faster than the light can travel between them, is to travel a narrower road than the strait line (bending space). Meaning we need to find a shorter route between two locations than the strait line, and that route need to be much smaller than the strait line for us to reach the destination faster than the light. Ok, lets assume we have an object travelling at the speed of light (regardless of all other laws). An observer sees the object travelling at the same speed as light and tries to apply a force to the object in the same direction as it travels. The speed of force is according to some C (speed of force = speed of light). The observer cannot accelerate the force to ever reach the object, they will have the same speed relative the observer. However the object travelling at C se the rest of the universe as standing still in time (because the rest of the universe is travelling at C relative the object). So if someone outside decide to apply a force to the object, will that ever happen according to the object itself (according to the object, there is no time in which an outsider can apply anything)? (I might be wrong!!!)
Hi all, SeekerOfTruth, "However, in the context of relativity, what does the word "rest" mean? I take it to mean that it is not in motion relative to the observer, but that does not imply the object is not in motion, only that the observer and the object are synchronized in motion. When you think about this, what does mass really mean then? What is the frame of reference for the definition of "rest"? Only the observer?" One of the fundamental concepts of all theories in physics is that there is no frame of reference that is "better" than all others (this implies that physics should be the same for everybody: when I see an apple falling towards the ground, then in your frame of reference that apple can't ofcourse be falling "away" from earth - or something along these lines). Hence, "rest" can only be defined the way you specified: an object is at rest for the observer if the observer measures "v = 0" for that object. If you would measure the mass of that object, then you would be measuring the restmass (often denoted m<sub>0</sub>). So you are correct in saying that "rest" is a relative concept. However, if someone else (another observer) would measure the restmass, then he would get exactly the same result m<sub>0</sub> (because to do that, that observer would also have to move "synchronously" with the object to measure). That is no longer true for (relativistic) mass m: in the definition of (relativistic) mass, a velocity appears, and it is obvious that velocities of an object can differ for different observers. The following example illustrates why there is an important difference: Suppose I am holding an apple in a train. The (relativistic) mass I would measure is: m = m<sub>0</sub> / sqrt( 1 - (v/c)<sup>2</sup>) = m<sub>0</sub> because in my frame of reference, v = 0 for the apple. Someone standing next to the railroad would measure a different (relativistic) mass because he sees the apple moving at a velocity v =/= 0. "Given an object traveling at the speed of light (assuming it could be brought to that speed), if a force was applied to the object in the direction of velocity, what would happen?" Then, on the whole issue of applying forces on objects that move at a velocity c: First of all, this is a hypothetical situation because of two reasons: - You cannot accelerate an object with restmass beyond c. Only objects with restmass m<sub>0</sub>=0 (such as fotons) can reach c. - You cannot apply a force to an object with restmass m<sub>0</sub> = 0, because F = m*a would require an infinite acceleration to give a finite, non-zero value for F. Now you can do two things: either you describe the whole thing in a classical Newtonian context where laws like "F = m*a" are valid. In that case, the speed of light c has no special significance (notions such as "nothing with restmass can travel at c" are only valid when working in a relativistic framework). So applying a force to an object with speed c would be the same as applying a force to an object that moves at 10 meters/sec. You simply accelerate it in the direction your force works in. This ofcourse doesn't answer the question "what will really happen when you perform the experiment", so let's try a more relativistic description: in that case you can make a lot of claims, simply because relativistically speaking no object with restmass can attain a speed of c. One claim could be "you cannot accelerate an object that moves with speed c", simply because forces propagate at the speed of light (this is an assumption btw) so your object would always outrun the force being applied to it. But in either case, I personnally wouldn't really trust claims that are replys to statements like "if I go at c and turn on my headlights" or "ok, we know it cannot happen but what if... ". Bye! Crisp
Special Relativity Only works for inertial frames of reference and is a 'local' theory. That is, if your frame is non-inertial, accelerating, it no longer holds and you need General Relativity. The odd thing is GR does allow things to go faster than light providing, again, they are not local. Local is usually taken as the Universe but there have been jets from active galactic nuclei detected whose velocity is greater than c. Its an optical illusion. As for warp bubbles and warp travel you should read this paper by Miguel Alcibierre
Crisp, First, thanks for the info. It gives me more to think about. Second, I understand that photons are believed to have no mass. However, I though I had recently read an article that states some physicists now believe photons might have some miniscule amount of mass. Have you any information or thoughts on this? Third, if photons have no mass, how do they impart energy to electrons through photoelectric effects such as those found in solor cells? Fourth, and here is the concept I am trying to get at, the theory of relativity relates mass, energy, and velocity to each other. Mass is somehow related to gravity through its effects on spacetime. A new theory has now linked gravity and magnetic fields and implies strongly bending magnetic fields exert a "force" on spacetime that in effect causes spacetime to "unbend" which implies that you could shield an object from the effects of gravity, and thereby impact the relationships described in Einstein's theory of relativity. If this theory is true, what are the implications to Einstein's theory of relativity and the relationships between mass, energy, and velocity?
Seeker I think you are thinking of Neutrinos. They where thought to be massless but recently are thought to have a small rest mass in the region of 0-3eV. As for photons and electrons interacting, that is the nature of quantum mechanics for you. Photons are the particle counterpart of light. As such they have energy and momentum that can be transfered in a collision. That bumf on magnetic fields and space time curvature does not affect Relativity. If you curve spacetime it stores energy, this is what you extract to accelerate and is how you 'feel' gravity. EM forces are larger than gravitational forces so two strong EM fields in a strongly curved region of spacetime will only get stronger. The energy from this can be used to further bend spacetime, if I read the paper properly. This is all within general relativity, mass/energy is used to bend spacetime, so why not the energy from another field.
Thed, Thanks for your thoughts. I am aware of the recent thoughts on Neutrinos having mass, but I remember reading an article somewhere that theorized photons also had mass and I will have to try and find it. What is the definition of momentum in the relativistic sense? Doesn't momentum imply mass in some manner? I think I can understand how a photon can interact with an electron in a quantum mechanics kind of way, imparting some of its energy to the electron through a superposition of quantum mechanical energy, but the concept of momentum to me implies mass. Can you tell me more of how mass relates to spacetime? I have to admit my last physics class was quite some time ago.
Seeker According to Special Relativity any object with restmass can not achieve lightspeed, it would require infinite energy. So, if a photon (light) had mass it could never reach light speed. A paradox solved by photons not having restmass. It's all to do with the famous E( γ ) = M( γ )c<sup>2</sup> where, γ = sqrt ( 1 - v<sup>2</sup> / c <sup>2</sup> ) You will see that in the limit v -> c γ = infinity so E above goes to infinity. Its the same, in way. According to the above equation energy and mass are interchangeable. A photon has energy so it has an affective mass and hence momentum. The proper equation is <a href="http://www.treasure-troves.com/physics/MomentumFour-Vector.html">found here as eq 8</a>. Rearranging this with m=0 you get E=pc. Only in the Newtonian sense. Einstein worked out that Energy can behave as mass. Hopefully you can see that mass and energy are interchangeable. Now that's a tricky one. In all honesty Physics can not explain why mass affects spacetime. It can describe it through Relativity but not explain it. It is assumed, from Newton, that gravity is related to mass but no one knows why. This is where the next great discovery is needed. There are rafts of ideas at the moment and they all relate to marrying quantum mechanics with Relativity. This is a topic unto itself.
Twas brillig and the slithy gauges did gire and gimble in the wabe. Mr. G. Have to admit that I am not hugely happy with invoking scalar quantum fields as the cause for mass. Yes, I do know that CERN reckon they may have seen one and the Higgs mechanism is used to describe the W and Z particles. Just seems more like a fad to use fields all the time.
Rotating universe The question of a rotating universe was asked on the SSSF, see link. Geraint is a cosmologist at the Anglo Australian Telescope in New South Wales. <a href=http://www2b.abc.net.au/science/k2/stn/posts/topic439125.shtm>http://www2b.abc.net.au/science/k2/stn/posts/topic439125.shtm</a> And <a href=http://www2b.abc.net.au/science/k2/stn/archive2001/posts/April/topic279977.shtm>http://www2b.abc.net.au/science/k2/stn/archive2001/posts/April/topic279977.shtm</a> And <a href=http://www.lns.cornell.edu/spr/2000-11/msg0029498.html>http://www.lns.cornell.edu/spr/2000-11/msg0029498.html</a>
