In Newtonian physics, the "inertia" of a particle may be regarded as its "resistance to acceleration".
In Special Relativity, "inertial resistance" is more than particle "inertia" and originates from Minkowski spacetime structure.
This is an avenue that you may like to explore.
Perhaps Einstein made a relevant statement when he said, "According to classical mechanics "velocity relativity" exists, but not "acceleration relativity".
As you may tell, I am way out of my Newtonian frame of reference!
This comparison is unscientific: if I arbitrarily reduce two highly complex different phenomena, e.g. put them in a box, then I can only explain them within the framework of the observation in the box. There is nothing left to explain.Einstein's equivalence principle
If I also call this misfortune a "principle", then it is intended to prevent criticism and discussion: this is anti-scientific;-)
Also clarifies the observer, the observation, always, generally. Rarely are events and observations properly analyzed and separated, which leads to accidents like this one.
By the way: What is part of an "inertial system" within Einsteins relativity theses - take a close look...
... closer
... closer
...-)
Galu, this comes back to inertial frame of reference (IFoR). Seems to my simple brain there is some sort of paradox here. On the one hand, all motion is relative, and thus all time is relative for non co-moving objects. By that I mean if I am moving at c and look at the watch on my wrist it will still tick away in seconds, but not for the distant observer where the hands will be frozen. However, if two bodies share the same IFoR and one is accelerated away, the energy transformed in the process is not relative despite the times on the clocks subsequently ticking at different rates and their motion with respect to each other being completely relative. So time and motion are relative but energy transformation is not, it is tied to a specific object? If this is not the case, I assume you could find a way in GR to ‘transfer’ the acceleration force to the reference clock to uphold the relative motion pillar in GR - but seems totally counterintuitive.
What am I missing here?
What am I missing here?
To recap, you have specified motion in a "flat spacetime", aka Minkowski spacetime, so we are dealing with special relativity.
Here's some information which comes highly edited from discussions on relativistic energy:
The rest mass of a particle is an unchanging quantity in the inertial frames in flat spacetime. However the total energy of the particle is frame-dependent.
Relative motion between two frames causes the observers in those frames to measure different values of the particle's energy.
For example, the energy in a particle's rest frame (as measured by an observer moving with the particle) is different from the energy in a local reference frame (as measured in the lab by a particle physicist who is not moving with the particle).
I hope this is of some help in solving your energy transformation conundrum which, I admit, greatly confuses me!
Let’s go back to this again. The non accelerated clock will feel no inertia (I called it ‘weight’ to link it to Einstein’s equivalence principle 1g thought experiments) but only the accelerated clock. But, you can choose either clock as a relative time and motion reference for the other post acceleration. I feel that the minute you talk about ‘the non accelerated clock feels nothing’ there is a conundrum there. This is flat space time. If the accelerated clock is chosen as the reference, the non accelerated one now has the kinetic energy that was imparted to the accelerated one.
This would seem to imply that kinetic energy is relative, but not rest mass energy or the energy used accelerating the one object. Other than that, surely this means the two situations are equivalent in order to uphold SR?
Let's look at the definition of inertia:
"Inertia is the natural tendency of an object to remain at rest or to continue moving with constant speed in a straight line."
The non-accelerated clock therefore has inertia, as does the accelerated clock.
In the accelerated frame, inertia results in a 'fictitious force', and it is to that you are referring when you say the accelerated clock "feels" inertia.
The non accelerated clock will only have the inertia it originally possessed before the other clock was accelerated surely?
Why is the inertia fictitious? It only arises when a real force is applied and once the force is removed, the energy used to apply the force is conserved as additional kinetic energy in the accelerated clock.
Why is the inertia fictitious? It only arises when a real force is applied and once the force is removed, the energy used to apply the force is conserved as additional kinetic energy in the accelerated clock.
Well, it can hardly change its inertia as that is a fixed property of the object.
I didn't say that. Inertia is real.
When you accelerate an object it feels like there is a force (which you seem to be mistakenly calling "inertia") opposing the accelerating force, but this force is fictitious.
It's like the force you feel in a moving car that pushes you back into your seat when the driver steps on the accelerator pedal. This fictitious force arises because the natural frame of reference in that situation is itself accelerating.
Inertia doesn't "arise" when a force is applied. It is an immutable property of matter as per the definition in my previous post.
Galu, fair enough - it’s an intrinsic property of any non zero mass in motion. But inertia will only manifest as a force when another force acts upon it. If I am cruising along at 60 MP I do not feel inertia and neither would any inanimate object. However, if I apply a force to that object, I would feel inertia manifest as a force - for example if I apply the brakes - hence my statement about inertia only arising when a force is applied to an object. There are no fictitious forces, only energy transformations.
(Kinetic energy perhaps encapsulates what it is).
(Kinetic energy perhaps encapsulates what it is).
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If you apply the brakes suddenly, your reference frame rapidly accelerates (decelerates) relative to you, giving rise to a fictitious force
This fictitious force is the perception that you are being pushed in the direction of the windscreen just before your head comes into contact with it.
That's why you should "Clunk Click Every Trip".
However, I must admit that there is no fictitious force in the situation you described where a clock is being accelerated. This acceleration must come about through a physical interaction from another object. Something has got to push the clock after all!
It seems we are both capable of mixing up our scientific metaphors!
I am talking about the interval between braking and the driver's head hitting the windscreen, not the subsequent interaction between head and windscreen.
To an observer traveling in the car's accelerating frame of reference, it appears that a force propels the driver towards the windscreen. This force is a fictitious or pseudo force as it does not arise due to any physical interaction between two objects.
To an outside observer in a stationary frame of reference, the driver is simply continuing to move with constant speed (due to his inertia) while the car decelerates.
Frames of reference, Bonsai, frames of reference!
To an observer traveling in the car's accelerating frame of reference, it appears that a force propels the driver towards the windscreen. This force is a fictitious or pseudo force as it does not arise due to any physical interaction between two objects.
To an outside observer in a stationary frame of reference, the driver is simply continuing to move with constant speed (due to his inertia) while the car decelerates.
Frames of reference, Bonsai, frames of reference!
We are well acquainted with the fact that the Earth has both a gravitational field and a magnetic field.
It has now been confirmed that our planet has an electric field, something that was hypothesised over 6 decades ago.
The electric field counters gravity at the Earth's poles where it propels ionised particles out of the atmosphere at supersonic speeds.
Further studies of the phenomenon are hoped to tell us more about the evolution of our precious atmosphere.
https://www.space.com/earth-planet-wide-electrical-field
It has now been confirmed that our planet has an electric field, something that was hypothesised over 6 decades ago.
The electric field counters gravity at the Earth's poles where it propels ionised particles out of the atmosphere at supersonic speeds.
Further studies of the phenomenon are hoped to tell us more about the evolution of our precious atmosphere.
https://www.space.com/earth-planet-wide-electrical-field
This paper is not really interesting: in the previous paper, you find this sentence:
"The discrepancy between receding and approaching objects is obvious, as it is harder to accelerate an object against its direction of movement than if it moves in the same direction." which is pivotal to the entire construction. I don't even agree with the statement in the relativistic setting with how I understand "harder". There is no comparison with known and measured general relativistic effects such as frame-dragging, where the same constant appears. With the shallowness of the work presented, I am confident, but not certain, a fatal inconsistency exist not too deep, but I am lazy at the moment to look for it. Properly debunking "theories" without using sweeping dogmatic statements is actually harder than it might look, but it always end up working... I do that sometimes as a challenge.
Moreover, with respect to the second paper, leptons, neutrinos, etc. do not have internal structure and still respond to gravity so the proposed explanation is at the very very best incomplete. Add to that that the articles in question are publish at a predatory pay-to-publish editor with articles of questionable quality and yeah...
"The discrepancy between receding and approaching objects is obvious, as it is harder to accelerate an object against its direction of movement than if it moves in the same direction." which is pivotal to the entire construction. I don't even agree with the statement in the relativistic setting with how I understand "harder". There is no comparison with known and measured general relativistic effects such as frame-dragging, where the same constant appears. With the shallowness of the work presented, I am confident, but not certain, a fatal inconsistency exist not too deep, but I am lazy at the moment to look for it. Properly debunking "theories" without using sweeping dogmatic statements is actually harder than it might look, but it always end up working... I do that sometimes as a challenge.
Moreover, with respect to the second paper, leptons, neutrinos, etc. do not have internal structure and still respond to gravity so the proposed explanation is at the very very best incomplete. Add to that that the articles in question are publish at a predatory pay-to-publish editor with articles of questionable quality and yeah...
;-)
“We have verified your results completely. It seems to me now that there can be absolutely no doubt, that you were completely correct in assuming that beta radiations are primarily inhomogenous. But I do not understand this result at all.” Lisa Meitner to Charles Ellis. 20.07.1929.
Lisa confirms the difference between the measurement, 0.35 MeV, and the calculation, 1.05 MeV, of 0.7 MeV energy release during radium decay. But even she does not doubt the validity of the equations; which are unscientific nonsense anyway!
Neutrinos, too, are the adaption of observation to incorrect theses and equations only;-)
“We have verified your results completely. It seems to me now that there can be absolutely no doubt, that you were completely correct in assuming that beta radiations are primarily inhomogenous. But I do not understand this result at all.” Lisa Meitner to Charles Ellis. 20.07.1929.
Lisa confirms the difference between the measurement, 0.35 MeV, and the calculation, 1.05 MeV, of 0.7 MeV energy release during radium decay. But even she does not doubt the validity of the equations; which are unscientific nonsense anyway!
Neutrinos, too, are the adaption of observation to incorrect theses and equations only;-)