B Why does it require an infinite amount of energy to reach the speed of light?

[jbriggs444]

It depends how you define "isolated system". E.g., some piece of matter gets a larger invariant mass when it gets warmer or a charged capacitor has a larger invariant mass than an uncharged one etc.

I've always understood "isolated" as the strongest form of a closed system there is. No mass transfer, no momentum transfer, no energy transfer, no charge transfer. Nothing gets in or out.

 

[Grasshopper]

I've always understood "isolated" as the strongest form of a closed system there is. No mass transfer, no momentum transfer, no energy transfer, no charge transfer. Nothing gets in or out.

I myself have wondered if that's even physically possible, with all the quantum weirdness. I'm of course fully ignorant about QM, but the thought has crossed my mind. Not that it matters, since in physics simplifying models are used to isolate particular paths of inquiry.

 

[jbriggs444]

I myself have wondered if that's even physically possible, with all the quantum weirdness. I'm of course fully ignorant about QM, but the thought has crossed my mind. Not that it matters, since in physics simplifying models are used to isolate particular paths of inquiry.

Yes. I agree. Perfect isolation is likely unachievable. But it is a useful ideal which we can approximate in practice.

 

[vanhees71]

Of course, in this idealized sense of "isolated system" the invariant mass is conserved, but it's not an independent conservation law but follows from energ-momentum conservation and the definition of invariant mass, $p_{\mu} p^{\mu}=m^2 c^2$, where $p$ is the total four-momentum of the isolated system.

 

[Dale]

Of course, in this idealized sense of "isolated system" the invariant mass is conserved, but it's not an independent conservation law but follows from energ-momentum conservation and the definition of invariant mass, $p_{\mu} p^{\mu}=m^2 c^2$, where $p$ is the total four-momentum of the isolated system.

Yes, which is precisely why I disagree with statements that mass is not conserved. If energy and momentum are conserved then conservation of mass follows. It is not independent so you cannot say that the former two hold and the latter does not.

Note further, that the idealized sense of isolated system is the same idealization for energy and momentum conservation. If you choose any non-ideal system where mass is not conserved then either energy or momentum (or both) will also not be conserved.

 

[vanhees71]

As I tried to write in my long posting above the difference between Newtonian and relativistic physics concerning mass, from the point of view of the underlying symmetry principles, is that in Newtonian mechanics there is an additional mass-conservation law and that this can only be understood from a quantum theoretical argument. This additional conservation law is rather a super-selection rule then a usual conservation law from Noether's theorem. In relativistic physics mass is a Casimir operator and thus specifies the (irreducible) representations of the Poincare group as any Casimir operator of a symmetry group does. So there is no additional indepednent conservation law but it follows from energy-momentum conservation. The main point, however, is that via these symmetry arguments it is clear that conceptually the mass is to be defined as a Casimir operator of the Poincare group and thus as a scalar quantity, and quantities like various "relativistic masses" from the very early days of relativity are conceptually superfluous.

 

[Dylan007]

I don't need equations, I would just like to pose a question which contradicts the above statement (I know I am wrong btw, I want to see where I am going wrong).My understanding of space (not near any gravity and therefore no spacetime curvature) is that a body in motion will continue to move at said speed unless acted on by another force. So let's use an example. Let's say I am moving at 10mph through space but I want to reach the speed of light. (Now I'm going to use fictious numbers and equations to keep the math simple). Let's say in my spaceship I fire off my rockets to increase the speed, which requires 5 amount of Newtons (or whatever else the metric is for force – it doesn't really matter for the point I'll make). And that 5 amount of Newtons increases my speed by 10mph, so I'm now I'm going at 20mph. At this point I stop the rockets and i continue indefinitely at 20mph. So I now apply another 5 Newtons to reach 30mph, and so on until I reach the speed of light. This does not require an infinite amount of energy.Now I know the above is wrong (for many reasons) but bear with me for a minute. So from E=mc2 (I think) it states that the reason we can’t reach the speed of light is because as you get closer to the speed of light your mass increases, and therefore requires infinitely more energy – I get that. But the first issue I have here is that I thought speed was all relative. So in my example above I know that I am wrong when I keep saying my speed in increasing. But if my 30mph is the equivalent of being still in space, then how can my ship gain mass when increasing in speed? and therefore need infinitely more energy if speed is relative? To demonstrate more, imagine nothing is close by to judge our relative speed to it. To put it another it seems that speed is relative to everything but not light. I have come to the conclusion that when we say we can’t reach the speed of light that maybe it actually means the acceleration to the speed of light - because to reach the speed of light (relative to another body) we’d have to accelerate at an insane amount (which would require a lot of energy). So my question is, is it more accurate when we say “it requires an infinite amount of energy to reach the speed of light” to change that to “it requires an infinite amount of energy to reach the speed of light”
Or have I completely missed the point? Where I am coming from is that there is no speed in space unless it’s relative to another object. The other thing that is weird, is that, if light speed is always constant how can light still travel at said speed if I were to speed up just half the speed of light in the same direction as the light beam? I should perceive the light traveling at half the speed of light but I know (from reading up on GR) that light is always the speed no matter the reference frame. The explanation to this is that apparently that time is slowed down the faster you move – but again, I thought speed was relative.

In SR, if I see you are moving at half the speed of light (c), I will also see your clock run slower such that you will measure the light moving away from you at the speed of light (c). So don't matter at what speed you are traveling, light will always travel at c.

So at rest, light will travel at 670 000 000 mph away from you. So you should increase your speed with 6.7E8 mph to reach the speed of light. But when you reach 300 000 000 mph, you will still measure the speed of light at 6.7E8 mph and therefor still need to increase your speed with 6.7E8 mph. Even if you reach a speed of 600 000 000 mph, the speed of light will still be 6.7E8m mph and so on.

From an observer at rest, it will look like as if your acceleration is decreasing as you approach the speed of light due to the fact that the observer is also seeing your clock running slower. For example if you are acceleraing at 100 mph per hour, you will increase 100mph every hour. But because the observer see your hour going slower than his own - he will also see you accelerating slower.

Interesting fact: An person that is constantly accelerating, will follow a hyperbolic path and not an parabolic path. The asymptotes of the hyperbole is the speed of light

 

[Dylan007]

I don't need equations, I would just like to pose a question which contradicts the above statement (I know I am wrong btw, I want to see where I am going wrong).My understanding of space (not near any gravity and therefore no spacetime curvature) is that a body in motion will continue to move at said speed unless acted on by another force. So let's use an example. Let's say I am moving at 10mph through space but I want to reach the speed of light. (Now I'm going to use fictious numbers and equations to keep the math simple). Let's say in my spaceship I fire off my rockets to increase the speed, which requires 5 amount of Newtons (or whatever else the metric is for force – it doesn't really matter for the point I'll make). And that 5 amount of Newtons increases my speed by 10mph, so I'm now I'm going at 20mph. At this point I stop the rockets and i continue indefinitely at 20mph. So I now apply another 5 Newtons to reach 30mph, and so on until I reach the speed of light. This does not require an infinite amount of energy.Now I know the above is wrong (for many reasons) but bear with me for a minute. So from E=mc2 (I think) it states that the reason we can’t reach the speed of light is because as you get closer to the speed of light your mass increases, and therefore requires infinitely more energy – I get that. But the first issue I have here is that I thought speed was all relative. So in my example above I know that I am wrong when I keep saying my speed in increasing. But if my 30mph is the equivalent of being still in space, then how can my ship gain mass when increasing in speed? and therefore need infinitely more energy if speed is relative? To demonstrate more, imagine nothing is close by to judge our relative speed to it. To put it another it seems that speed is relative to everything but not light. I have come to the conclusion that when we say we can’t reach the speed of light that maybe it actually means the acceleration to the speed of light - because to reach the speed of light (relative to another body) we’d have to accelerate at an insane amount (which would require a lot of energy). So my question is, is it more accurate when we say “it requires an infinite amount of energy to reach the speed of light” to change that to “it requires an infinite amount of energy to reach the speed of light”
Or have I completely missed the point? Where I am coming from is that there is no speed in space unless it’s relative to another object. The other thing that is weird, is that, if light speed is always constant how can light still travel at said speed if I were to speed up just half the speed of light in the same direction as the light beam? I should perceive the light traveling at half the speed of light but I know (from reading up on GR) that light is always the speed no matter the reference frame. The explanation to this is that apparently that time is slowed down the faster you move – but again, I thought speed was relative.

With regard to increasing of mass, the notion that your mass increases as you approach the speed of light is a bit misleading (or leads to confusion)

From an observer at rest it is appearing that your mass is increasing as you approach the speed of light, because you appear to accelerate less (to the same force) as you approach the speed of light. From your own perspective it won't appear that your mass is increasing.

But relativistic mass becomes quite messy further on. So it is not a concept worth using: it is better to change the equation of momentum to momentum = gamma x mass x velocity

 

[Hornbein]

In my opinion Einstein's 1905 paper remains the simplest and clearest explanation.

To make a long story very short the basic idea is that the laws of physics are the same in every frame of reference. Especially electricity and magnetism. Given this, special relativity was deduced. The math is quite simple, basically high school trigonometry. The difficulty lay in persuading people that the math matched reality.

 

[PeterDonis]

@Dylan007 please do not quote an entire post when responding. Only quote the particular parts of the post that you are responding to.

 

[vanhees71]

In my opinion Einstein's 1905 paper remains the simplest and clearest explanation.

To make a long story very short the basic idea is that the laws of physics are the same in every frame of reference. Especially electricity and magnetism. Given this, special relativity was deduced. The math is quite simple, basically high school trigonometry. The difficulty lay in persuading people that the math matched reality.

Historically that's not entirely true, because almost immediately Einstein's view was accepted. The math was there even before (Lorentz, Poincare) but not the ingeniously simple physical interpretation of Einstein's 1905 paper. Immediately leading theorists of their time like Planck, von Laue, and Sommerfeld adapted these ideas and worked with them.

There were of course opponents among the physicists like the erratic ideologists of the "Deutsche Physik" movement like Lennard and Stark.

The greatest obstacle, however, have been philosophers. Particularly Bergson could never accept the notion of time according to the relativity theories. This had the bizarre consequence that Einstein did not get his Nobel prize for relativity, and that's even explicitly stated on the Nobel certificate.