[QUOTE=Trumple;28966161]Not true...
Take for example a football of mass 1kg
The kinetic energy is one form of energy the ball has, given by 0.5mv^2
When stationary, the KE of the football is 0J (0.5x1x0)
When moving at say 10 m/s, the KE is: 50J (0.5x1x10^2)
Since E=mc^2
m= E/c^2
So at a greater velocity, the mass of the ball is larger. True, not much larger when you factor in gravitational potential energy etc. but it is larger.[/QUOTE]
No you are wrong. The energy of that football at [b]rest[/b] is E=mc². That is the restmass energy.
When it moves the correct formula is
[img]http://math.daggeringcats.com/?E=\frac{m c^2}{\sqrt{1 - \frac{v^2}{c^2}}[/img].
Also you should use the term of energy-increase and not mass-increase. The only important mass is the restmass. Something like a "relativistic mass" increase is in physical terms bullshit because it would also mean mass was time dependent (since velocity changes over time and so would a "relativistic mass") which also means that e.g. newtons momentum law [img]http://math.daggeringcats.com/?p = \frac{\mathrm{d}}{\mathrm{d} t} m x[/img] would become [img]http://math.daggeringcats.com/?p = (\frac{\mathrm{d}}{\mathrm{d} t} m) x + m (\frac{\mathrm{d}}{\mathrm{d} t} m) x[/img] -> A mess.
Or in other words: Something like a "relativistic mass" is totally making physical calculations more complicated so you better associate the lorentz-boost factor to the energy and not the mass.
I could go deeper since I'm actually studying physics now for 5 years and doing my Master right now, but I really doubt you would understand it.
[QUOTE=sergeantsmiles;28964589]My theory, you can't change the past, anyone who attempts to stop an event will inadvertently cause it to happen.
Also, I somehow worked it out that time wasn't linear, and that the events of the future had already happened :v:[/QUOTE] It is currently believed that whenever you go back in time you create another dimension that does not effect the one you came from meaning you can kill your own grandfather.
Pretty nifty stuff.
I never understood why people seem to think photons gain mass as a result of mass-energy equivalence.
The speed of light is the limit for a reason.
What would happen if photons did gain (conventionally understood) mass?
[QUOTE=ThePuska;28967999]Another thing I don't quite understand is this: can gravity keep orbits stable? If gravity can't act immediately between two masses, circular orbits at least shouldn't remain stable as gravity doesn't pull the objects exactly towards the barycenter.[/QUOTE]
If you consider gravitation as an intrinsic property of spacetime being curved, the objects move along trajectories in that curved spacetime. The curvature itself can only change with the speed of light as gravitation "moves" with that speed. So the object moves in something which "was already there".
And even if you use a modern hypothesis which involves quantized gravitation (particles), you get the same results.
[QUOTE=JgcxCub;28952643]Hmmm, well, I (for one?) am a firm disbeliever in special relativity.
Speed can only be taken in a specific frame of reference. How can we say that there's a universal speed limit when we're probably surpassing that speed on a large enough level (that is, speed relative to the earth, then the sun, then the system, the cluster, the galaxy, the galaxy cluster, etc)?[/QUOTE]
and I thought creationists were stupid
[editline]3rd April 2011[/editline]
[QUOTE=Contag;28970503]I never understood why people seem to think photons gain mass as a result of mass-energy equivalence.
The speed of light is the limit for a reason.
What would happen if photons did gain (conventionally understood) mass?[/QUOTE]
They can't, ever. Although, as I understand it, they have momentum, due to shenanigans that I haven't learned about yet.
After reading this thread up to this point, I can honestly say that I believe the first time machine will be built by (some of) the people in this thread. :v:
[QUOTE=Turnips5;28971382]
They can't, ever. Although, as I understand it, they have momentum, due to shenanigans that I haven't learned about yet.[/QUOTE]
I know, but could the more physics inclined (I'm looking at you Mr. postgrad) sketch out a rough idea of the largest changes if it were true?
[editline]4th April 2011[/editline]
OP, if you want a real mindfuck theory, look into the school of thought that argues that the key reason why women are oppressed is "our linear concept of time" and "the Cartesian (X,Y,Z)" way in which we view bodies.
I shit you not.
[QUOTE=aVoN;28970178]I could go deeper since I'm actually studying physics now for 5 years and doing my Master right now, but I really doubt you would understand it.[/QUOTE]
I find this very interesting, so if you are able and willing to go deeper, while keeping it at an understandable level, I would appreciate it.
Don't know about the others in this thread, tho.
[QUOTE=Dryvnt;28972499]I find this very interesting, so if you are able and willing to go deeper, while keeping it at an understandable level, I would appreciate it.
Don't know about the others in this thread, tho.[/QUOTE]
Yes, please do.
[QUOTE=Dryvnt;28972499]I find this very interesting, so if you are able and willing to go deeper, while keeping it at an understandable level, I would appreciate it.
Don't know about the others in this thread, tho.[/QUOTE]
Well this requires a lot of writing formulas for me :/
Basically most stuff like Newtons laws are still valid when working with Relativity. As instance I would name force to be the derivative of momentum concerning time.
[img]http://math.daggeringcats.com/?F = \frac{\mathrm d}{\mathrm d t} p[/img]
Also we know how energy increases concerning speed:
[img]http://math.daggeringcats.com/?E = \frac{m_0 c^2}{\sqrt{1 - \frac{v^2}{c^2}}}[/img]
If you now associate the Lorentz-boost-factor [img]http://math.daggeringcats.com/?\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/img] to the mass and call it "relativistic mass" you get
[img]http://math.daggeringcats.com/?m'(v) = m_0 \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/img] where [img]http://math.daggeringcats.com/?m_0[/img] is the restmass.
[b]Now back to Newtons laws:[/b]
The relativistic momentum is defined as [img]http://math.daggeringcats.com/?p = m_0 \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} v[/img]
You have two situations now: Either you work with a "relativistic mass" or you do it right.
[u]"Relativistic Mass" bullcrap[/u]: You associate the boost-factor to the mass
[img]http://math.daggeringcats.com/?p = m' v = m_0 \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} v[/img]
This leads to a formula for the force as:
[u]"Relativistic Mass" bullcrap way[/u]
[img]http://math.daggeringcats.com/?F = \frac{\mathrm d}{\mathrm d t} p = \frac{\mathrm d}{\mathrm d t} (m' v)= (\frac{\mathrm d}{\mathrm d t} m') v + m' \frac{\mathrm d}{\mathrm d t} v[/img] (Chain rule: since the "relativistic mass" now depends on the velocity and the velocity by time, you need to apply the chain rule).
This makes most stuff look and work really complicated.
[u]Right way[/u]: You just accept that there is only a restmass.
[img]http://math.daggeringcats.com/?F = \frac{\mathrm d}{\mathrm d t} p = \frac{\mathrm d}{\mathrm d t} m_0 v' = m_0 \frac{\mathrm d}{\mathrm d t} v'[/img]
Here the lorentz boost factor is associated to the effective velocity [img]http://math.daggeringcats.com/?v' = v \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/img].
This is just "hiding" of Lorentz factor, yes. But if you don't do it, your formulas explode due to chain rules and just because you want to have your mass dependent on velocity.
[b]Another easier way to understand:[/b]
A particle at a speed v has the energy [img]http://math.daggeringcats.com/?E = \frac{m c^2}{\sqrt{1 - \frac{v^2}{c^2}}}[/img]
Then it has more energy to create a particle at a higher mass equivalent to the "relativistic mass" bullcrap, yes. But that does not say the initial particle has a higher mass at those speeds itself! Also you made this link using the energy equation and not by "mass".
In short: Do not associate the Lorentz Boost Factor to the mass to call it Relativistic Mass.
You can even go deeper using Lagrangian mechanics but that's definitely way to high for everyone except those who were studying physics for more than 3 semesters.
Studying for a relativity exam I have tomorrow right now, actually. First introduction to relativity done with tensors.
[editline]3rd April 2011[/editline]
[QUOTE=Contag;28971594]I know, but could the more physics inclined (I'm looking at you Mr. postgrad) sketch out a rough idea of the largest changes if it were true?[/QUOTE]
According to my electricity and magnetism professor, who is a particle physicist, it helps a shit ton to have mass be Lorentz invariant when you're dealing with quantum field theory.
So if you made the speed of light faster.
Everything would be motherfucking heavy.
...No.
[editline]3rd April 2011[/editline]
In fact, even if relativistic mass existed, if the speed of light was faster, objects would have to be moving at a higher velocity to get the same Lorentz factor. Everything would, in fact, be LESS heavy.
[QUOTE=JohnnyMo1;28975575]...No.
[editline]3rd April 2011[/editline]
In fact, even if relativistic mass existed, if the speed of light was faster, objects would have to be moving at a higher velocity to get the same Lorentz factor. Everything would, in fact, be LESS heavy.[/QUOTE]
I haven't had sleep for 2 days. I'm not really in the best state of mind for any type of logic.
relativity is a pretty cool guy he fucks with your mind and he doesn't afraid of anything
[QUOTE=meppers;28960632]So how come Kirk and Spock don't age funny on the enterprise?[/QUOTE]
Because they're travelling within a warp bubble.
They aren't actually moving, at all, they're bending space around them.
[QUOTE=Opacity;28950304]i thought everyone knew about this already[/QUOTE]
Thanks, Einstein.
-snip- I'll add it to OP
Why are we worrying about the science behind how time and the universe works, when we still haven't even discovered a solution to not blowing each other up...
[QUOTE=ElChrisman99;28991796]Why are we worrying about the science behind how time and the universe works, when we still haven't even discovered a solution to not blowing each other up...[/QUOTE]
Because it is awesome.
[QUOTE=ElChrisman99;28991796]Why are we worrying about the science behind how time and the universe works, when we still haven't even discovered a solution to not blowing each other up...[/QUOTE]
You can't remove instinct, son.
[QUOTE=aVoN;28974834]Well this requires a lot of writing formulas for me :/
Basically most stuff like Newtons laws are still valid when working with Relativity. As instance I would name force to be the derivative of momentum concerning time.
[img_thumb]http://math.daggeringcats.com/?F = \frac{\mathrm d}{\mathrm d t} p[/img_thumb]
Also we know how energy increases concerning speed:
[img_thumb]http://math.daggeringcats.com/?E = \frac{m_0 c^2}{\sqrt{1 - \frac{v^2}{c^2}}}[/img_thumb]
If you now associate the Lorentz-boost-factor [img_thumb]http://math.daggeringcats.com/?\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/img_thumb] to the mass and call it "relativistic mass" you get
[img_thumb]http://math.daggeringcats.com/?m'(v) = m_0 \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/img_thumb] where [img_thumb]http://math.daggeringcats.com/?m_0[/img_thumb] is the restmass.
[B]Now back to Newtons laws:[/B]
The relativistic momentum is defined as [img_thumb]http://math.daggeringcats.com/?p = m_0 \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} v[/img_thumb]
You have two situations now: Either you work with a "relativistic mass" or you do it right.
[U]"Relativistic Mass" bullcrap[/U]: You associate the boost-factor to the mass
[img_thumb]http://math.daggeringcats.com/?p = m' v = m_0 \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} v[/img_thumb]
This leads to a formula for the force as:
[U]"Relativistic Mass" bullcrap way[/U]
[img_thumb]http://math.daggeringcats.com/?F = \frac{\mathrm d}{\mathrm d t} p = \frac{\mathrm d}{\mathrm d t} (m' v)= (\frac{\mathrm d}{\mathrm d t} m') v + m' \frac{\mathrm d}{\mathrm d t} v[/img_thumb] (Chain rule: since the "relativistic mass" now depends on the velocity and the velocity by time, you need to apply the chain rule).
This makes most stuff look and work really complicated.
[U]Right way[/U]: You just accept that there is only a restmass.
[img_thumb]http://math.daggeringcats.com/?F = \frac{\mathrm d}{\mathrm d t} p = \frac{\mathrm d}{\mathrm d t} m_0 v' = m_0 \frac{\mathrm d}{\mathrm d t} v'[/img_thumb]
Here the lorentz boost factor is associated to the effective velocity [img_thumb]http://math.daggeringcats.com/?v' = v \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/img_thumb].
This is just "hiding" of Lorentz factor, yes. But if you don't do it, your formulas explode due to chain rules and just because you want to have your mass dependent on velocity.
[B]Another easier way to understand:[/B]
A particle at a speed v has the energy [img_thumb]http://math.daggeringcats.com/?E = \frac{m c^2}{\sqrt{1 - \frac{v^2}{c^2}}}[/img_thumb]
Then it has more energy to create a particle at a higher mass equivalent to the "relativistic mass" bullcrap, yes. But that does not say the initial particle has a higher mass at those speeds itself! Also you made this link using the energy equation and not by "mass".
In short: Do not associate the Lorentz Boost Factor to the mass to call it Relativistic Mass.
You can even go deeper using Lagrangian mechanics but that's definitely way to high for everyone except those who were studying physics for more than 3 semesters.[/QUOTE]
Einstein would agree with you.[INDENT] "It is not good to introduce the concept of the mass [IMG]http://upload.wikimedia.org/math/f/b/6/fb64b7dab77855c07b3384a20fbf7654.png[/IMG] of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ [I]m[/I]. Instead of introducing [I]M[/I] it is better to mention the expression for the momentum and energy of a body in motion."
– Albert Einstein in letter to Lincoln Barnett
[/INDENT]
However, I have the Feynman Lectures here right in front of me, and it says quite opposite.
"Newton’s Second Law, which we have expressed by the equation
[IMG]http://upload.wikimedia.org/math/6/3/f/63f81c7fc0947599d7793204b766bea5.png[/IMG]
was stated with the tacit assumption that m is a constant, but we now know that this is not true, and that [B]the mass of a body increases with velocity[/B]. In Einstein’s corrected formula m has the value
[IMG]http://www.gravitywarpdrive.com/NGFT_Equations/Relativistic_Mass.gif[/IMG]
where the "rest mass" m0 represents the mass of a body that is not moving and c is the speed of light, which is about 3.10 5 km.sec−1 or about 186 000 mi.sec−1."
Is there something I'm misinterpreting here because Professor Feynman is quite brilliant, yet Einstein himself is saying something otherwise.
The way Feynman writes it is because he didn't seem to introduce the Lagrangian of a relativistic particle which directly leads to the momentum and therefore force with the lorentz factor as correction.
It's easier to say/write "bla bla, mass increase, so use this factor" (which is actually "bullshit") rather than doing the math (Lagrangian mechanics of relativistic particle, derive canonical momentum and move on) which does not say "hey, it must be linked to the mass".
[QUOTE=aVoN;28999901]The way Feynman writes it is because he didn't seem to introduce the Lagrangian of a relativistic particle which directly leads to the momentum and therefore force with the lorentz factor as correction.
It's easier to say/write "bla bla, mass increase, so use this factor" (which is actually "bullshit") rather than doing the math (Lagrangian mechanics of relativistic particle, derive canonical momentum and move on) which does not say "hey, it must be linked to the mass".[/QUOTE]
Yes, upon further reading, I have found that what you are saying is correct.
Out of interest, can someone explain how the fact that if one twin is travelling in one direction relative to the other, then the second twin could also be treated as travelling away from the first twin in the opposite direction, therefore depending on which reference frame you consider it from, a different person would appear to age. Is it something to do with the change of intertial frame when they change direction?
[QUOTE=Sh33p;29000446]Out of interest, can someone explain how the fact that if one twin is travelling in one direction relative to the other, then the second twin could also be treated as travelling away from the first twin in the opposite direction, therefore depending on which reference frame you consider it from, a different person would appear to age. Is it something to do with the change of intertial frame when they change direction?[/QUOTE]
Yes, it's to do with the acceleration. That breaks the symmetry (it's not an inertial frame).
[QUOTE=Sh33p;29000446]Out of interest, can someone explain how the fact that if one twin is travelling in one direction relative to the other, then the second twin could also be treated as travelling away from the first twin in the opposite direction, therefore depending on which reference frame you consider it from, a different person would appear to age. Is it something to do with the change of intertial frame when they change direction?[/QUOTE]
The twins 'paradox' is the story I posted in the OP with Face and Punch.
Now, the reason it is a paradox is because: who is really moving away from who? While Punch is 'apparently' moving away from Face (Who is left on Earth), it could also be seen that Face is actually the one moving!
So in the equation:
[img]http://hendrix2.uoregon.edu/~imamura/123/lecture-9/TimeDilation.gif[/img]
What would you use for the 'proper' time, t? It depends on who's frame of reference you are measuring, but the paradox is: who is the one who will age and who will stay younger?
This was a question that arose which seemingly defeated the theory of relativity- however, when the restrictions of the theory are applied, it is clear to see why the theory of special relativity still holds:
The theory ONLY applies to inertial frames of reference (I.e ones that are not accelerating)
If we look at our example, Punch has been accelerating and decelerating towards the speed 0.95c (and back to 0 then back to 0.95 c again) and so he is not in an inertial frame of reference, therefore he does indeed age less than his twin, Face, in the same amount of 'real' time
Well, there you go. Another interesting snippet!
Hey guys give me enough clocks and I'll send half of them to space.
[editline]5th April 2011[/editline]
FOR SCIENCE
Sorry, you need to Log In to post a reply to this thread.
