The main problem seems to be that I've been using the equation:
(delta)t' = (delta)t/(1-(u^2)/(c^2))
The time dilation formula isn't adequate for this problem, for the reason you've already mentioned. You need to use the Lorentz Transformation.
Moderators: gmalivuk, Moderators General, Prelates
The main problem seems to be that I've been using the equation:
(delta)t' = (delta)t/(1-(u^2)/(c^2))
Plamo wrote:Relativity has been bothering me, mainly in the form of simultaneity, I'll take the example from one of Brian Greene's books:
Two guys are on a train, this train is fast moving (say, 7/8ths the speed of light) they are several meters apart.
They each have a stopwatch, which they agree to start when they see the light of a light bulb turn on.
The mediator on the train turns on the light, and, as relativity states, they start their watches at the same time from the perspective of the mediator.
The second mediator, standing on the train station that the train happens to pass by, however, disagrees, stating that the clocks were not started at the same time, as the light took longer to reach the guy on the front of the train, as it had to catch up to him at difference of 1/8th the speed of light, whereas the guy on the back approached the light at a combined speed of 15/8ths of the speed of light.
Now, I understand that simultaneity is relativistic, and each point of view has equal merit, and is considered true. For the first mediator, the clocks have the same time. For the second mediator, the clock at the front of the train will be behind than that of the back of the train, as I understand it.
My question is, what happens when the 1st mediator and his two clock bearing friends hop off the train, and meet the second mediator in the town between the two stations for some lunch and tea? Will the clocks be in synchronization, or will one be slower than the other?
My hypotheses are that either:
a) The deceleration of the train causes reverse time dilation, or something of the effect, causing the clock on the front of the train to 'catch up' to the other clock, resulting in the clocks to be simultaneous from the perspective of the stationary (No pun intended) observer
b) Greene(or I) is(am) missing some information or mechanic, or the experiment has been simplified to the point of inaccuracy
In any case, I'd love this experiment to be explained to me.
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Belial wrote:You are the coolest guy that ever cooled.
I reiterate. Coolest. Guy.
phlip wrote:Something to consider is that if two events happen at the same time and in the same place, then all observers will agree that they coincide. Like, if two cars crash, all observers will agree that the cars were trying to be at the same place at the same time, there won't be any observers that think that the collision just didn't happen. So, for instance, "the light reaches guy 1" and "guy 1 signs" are two events that happen at the same place at the same time... so everyone will agree they happen at the same time. We can't have one observer thinking the person signs before the light reaches them, and another observer thinking they sign after.
Sir_Elderberry wrote:After all, otherwise the only conclusion the man on the platform can make is that one head of state cheated.
thefume79 wrote:OK, so what happens if it was a mechanical trigger (like 2 mediators walking from the center of the table and tapping the heads of state on the shoulder or something) instead of a light bulb? Would the platform guy still observe a difference in signing times (even if it was really small)?
thefume79 wrote:I just don't see what the light bulb has to do with anything.
thefume79 wrote:Is the train distorted from front to back?
thefume79 wrote:Or is it how the photons are reaching the platform? Does it matter where the platform is?
thefume79 wrote:But basically if the front and back wall of the train had a clock, it would give the same to people within the car, but different times to the platform? Even if the platform viewed them from an equidistant?
thefume79 wrote:and THANKS to both of you!
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Herman wrote:Inspired by the "Certainty" thread:
Quantum mechanics works for macroscopic ("everyday") stuff too. In fact it makes more accurate predictions than classical mechanics. We use classical mechanics because it's a good approximation and the math is easier. There is no sharply defined "quantum realm." The border between quantum and macroscopic phenomena is a convenient fiction and is subject to context, like the border between physics and chemistry.
doogly wrote:Meteorswarm wrote:gmalivuk wrote:Meteorswarm wrote:conservation of energy seems to say you should have enough energy to overcome the black hole's pull, since you have your speed + whatever GPE you'd lose in approaching it. What gives?
Doesn't matter how much energy you have: if it's finite, it's not enough to overcome the black hole's pull.
But shouldn't you gain precisely as much energy as you'd need to get out by falling in in the first place?
That's an awfully Newtonian way of thinking, and it just doesn't apply here.
Magnanimous wrote:(fuck the macrons)
eSOANEM wrote:inertia is the resistence to acceleration that is associated with mass.
as mass increases as velocity does, so does inertia. This is the reason that your velocity cannot exceed the speed of light as an object exerting say 100N of force with a rest mass of 1Kg, the object starts accelerating at 100ms^-2 but by its mass then increases and the acceleration decreases.
mass is given by the equation
m_{0}(1-V^{2}/C^{2})^{-1/2} where m_{0} is the rest mass.
Magnanimous wrote:(fuck the macrons)
eSOANEM wrote:I am referring to relativistic mass as this is the only mass that is linked to inertia. A better question than what is the benefit of talking about relativistic mass is what benefit is there to talking about rest mass?
sikyon wrote:So if I were to say... that something had no inertia, would that implyno rest mass?they could go faster than light?
sikyon wrote:So if I were to say... that something had no inertia, would that implyno rest mass?they could go faster than light?
Charlie! wrote:sikyon wrote:So if I were to say... that something had no inertia, would that implyno rest mass?they could go faster than light?
Inertia is kinda more related to energy. No inertia (no resistance to change in velocity) means no energy, which makes it a little say it exists at all. So sure, you can have your thing with no energy go as fast as you want
Magnanimous wrote:(fuck the macrons)
eSOANEM wrote:Charlie! wrote:sikyon wrote:So if I were to say... that something had no inertia, would that implyno rest mass?they could go faster than light?
Inertia is kinda more related to energy. No inertia (no resistance to change in velocity) means no energy, which makes it a little say it exists at all. So sure, you can have your thing with no energy go as fast as you want
a photon has 0 mass but does transmit energy so that isn't entirely true.
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eSOANEM wrote:I'm not entirely sure what the wikipedia article means when it talks about inertia as a geodesic deviation but the way I've always been taught of inertia in relativity is that it no longer refers to an object's resistance to acceleration but rather how closely it adheres to the path of a light beam on the same initial trajectory, alternatively how easily the object is moved by the curvature of spacetime and hence leads to my first relativistic definition.
Eebster the Great wrote:I think people here have an antiquated conception of inertia. In classical mechanics, m is called inertia because it is inversely proportional to acceleration, by the simple equation: [math]\textbf{F} = \frac{d \textbf{p}}{dt} = \frac{d}{dt} m \textbf{v} = m \frac{d \textbf{v}}{dt} = m \textbf{a}[/math] Clearly, this does not apply in SR, because momentum is not mv, but [math]\textbf{p} = γm\textbf{v} = \frac{m\textbf{v}}{\sqrt{1-\frac{v^2}{c^2}}}[/math] Even if we define [imath]γm = m_{rel}[/imath], that doesn't help much because [math]\textbf{F} = \frac{d \textbf{p}}{dt} = γ^3 m \textbf{a} \ne m_{rel} \textbf{a}[/math] So clearly m_{rel} isn't really "inertia" either. Since acceleration depends not only on force and mass, but also on speed, no one quantity adequately describes inertia in SR as it did in classical mechanics.
Of course, that doesn't mean we can't come up with new conceptions of what "inertia" means, but if we do that, why wouldn't we just use rest mass? And as it is, "mass" is almost universally understood to mean "rest mass," and the term "relativistic mass" is essentially deprecated.
GMontag wrote:We don't need a new conception of inertia for SR. The old one works just fine. Its the conceptions of force, velocity, and acceleration that have to change. F = dp/dt = ma works just fine in SR as long as F, p, and a are all four-vectors.
makc wrote:hey people, I have a question about observable universe horizon - can things cross it in/out in finite time? for example, would light of source crossing out be basically red-shifted out of existence? is there existing accurate analysis of this somewhere, or do I have to actually take LCDM equations and solve it myself (not really trust myself to do this)?
Wolydarg wrote:That was like a roller coaster of mathematical reasoning. Problems! Solutions! More problems!
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Fat Tony wrote:According to the Law of Conservation of Energy, a gun firing a bullet should cause the gun to have a momentum equal in magnitude to that of the bullet. Why, then, can a human shoulder easily stop a recoiling rifle with no penetration of the skin much more easily than it could a bullet?
Edit: Nevermind, I think I figured it out. The butt of the rifle distributes the force across a larger surface, lowering the pressure. Something along those lines?
thoughtfully wrote:Another thing: according to Conservation of Momentum, the sum of the momenta of the gun and the bullet will be the same before and after the shot. Momentum is mass times velocity. The mass of the gun (or gun plus the shooter's body, if the gun is well braced) is much greater than the mass of the bullet, so the change in velocity is much smaller.
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other wrote:
3) the energy content of a photon depends on the reference frame in which the measurement is made, so two reference frames can be designed such that observer A measures the photon as having sufficient energy to decay, while observer B does not. In such a pair of frames, if A actually does observe a decay in this mode, what does B observe? do the set-up requirements prevent A from telling B that the decay occured and then recieving a reply?
crazyjimbo wrote:So physics still works... phew. I'm sure one day someone will ask a question like this and everyone will just go 'well f***... it's broken'
crazyjimbo wrote:other wrote:
3) the energy content of a photon depends on the reference frame in which the measurement is made, so two reference frames can be designed such that observer A measures the photon as having sufficient energy to decay, while observer B does not. In such a pair of frames, if A actually does observe a decay in this mode, what does B observe? do the set-up requirements prevent A from telling B that the decay occured and then recieving a reply?
The rest frame makes things simple since we only need to deal with the rest masses of the produced particles. If we move to another frame then the produced particles will need to be created with additional energy since they will be be moving in the new frame. This energy will be the same as that gained by the photon by moving to the new frame.
So physics still works... phew. I'm sure one day someone will ask a question like this and everyone will just go 'well f***... it's broken'
PM 2Ring wrote:As mentioned, a photon in free space can't decay into a electron-positron pair. A high energy photon passing close to a nucleus can induce pair production, since it's interacting with the magnetic field of the nucleus. The nucleus is also involved in momentum conservation. (On a related note, a photon can't interact with a free electron.)
Going in the other direction, a electron-positron pair will decay into a minimum of two photons; the number will be odd or even depending on whether the lepton spins are parallel or anti-parallel. See the Wikipedia article on Positronium for details.
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