Gaining Kinetic Energy Through Time: Explained

[pmb_phy]

The 4-vector is a tensor, (but i imagine you're referring to the symmetric (0,2) rank tensor that is commonly called the stress-energy tensor.

Yup. Sorry. Thanks for the clarification.

It does simplify matters to talk about point particles, ..

So long as the domain of applicability is noted as it must be with all definitions. Its rarely, if ever, noted that a second rank tensor is required in general. I know only of Einstein, Rindler and Tolman to make this statement.

In fact it is clearly emphasised when discussing the field equations for the metric; this tensor is a clear feature of the equation describing (what is commonly called) "mass-energy" (but of course it describes more than that) of the system.

What does the metric tensor have to do with it? I was referring to special relativity only and not GR.

To make sure we're on the same page please see the example in SR that I worked out.

http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

Thanks

Pete

 

[jtbell]

But if things all depend on who's looking at them, then the whole universe is in chaos. In that case, you could basically move planets just by looking at them as you rush past in your spaceship.

But this is true in Newtonian mechanics too. It wasn't new with Einstein.

 

[nemosum]

Quote:
Originally Posted by nemosum
But if things all depend on who's looking at them, then the whole universe is in chaos. In that case, you could basically move planets just by looking at them as you rush past in your spaceship.

But this is true in Newtonian mechanics too. It wasn't new with Einstein.

But the universe ISN'T in chaos! Thing DON'T just fly around because someone looked at them!

 

[daniel_i_l]

These are possible factors in Relativity Experiments using Watches so there can be an error factor involved.

If during motion with constant velocity different watches can give different results, than that could be a way that an observer could tell if he is moveing or not, by comparing two watches? In motion with constant velocity all kinds of watches must give the same time.

 

[daniel_i_l]

But the universe ISN'T in chaos! Thing DON'T just fly around because someone looked at them!

It is true that an observer moving at a constant speed past a star is jusified to say that he is at rest and the star is moving past him. But that doesn't mean that the star is flying around the universe, relative to you, the whole universe is moving past you but it is at rest relative to itself (two stars that are moveing relative to you are at rest relative to each other) so there is no chaos, but all views are correct.

 

[masudr]

But the universe ISN'T in chaos! Thing DON'T just fly around because someone looked at them!

No one ever said that. There are (at least we think so, and have found most of these) strict rules as to how the universe behaves, and very few of them permit things "flying around just because someone looked at them" (in certain limits anyway, esp. in the relativistic limit).

 

[masudr]

I was referring to special relativity only and not GR.

Even in SR, for example, classical electrodynamic field theory, we are taught that we require the stress energy tensor to describe the 4-Lagrangian. Similarly, we are taught that Noether's theorem comes out of the fact that the 4-divergence of the stress energy tensor is 0. So I feel that there is sufficient emphasis on the fact that the stress energy tensor is required to describe a system.

Furthermore, in your web page, you are describing a box. And E=mc^2 only applies to particles and in it's own rest frame. Particles in general are constrained by E^2 = p^2 + m^2 (where I have set c=1).

 

[pmb_phy]

So I feel that there is sufficient emphasis on the fact that the stress energy tensor is required to describe a system.

You'd think so. But the problem is that people always ignore that fact. I see it on a constant basis in my travels in SR (last 15 years).

Furthermore, in your web page, you are describing a box. And E=mc^2 only applies to particles and in it's own rest frame. Particles in general are constrained by E^2 = p^2 + m^2 (where I have set c=1).

That is incorrect. What "E = mc²" means and in what frame it holds will depend critically on how "m" is defined. It seems to me that you're using the convention wherein "m" means "rest mass." I do not follow that convention (For many many reasons which I've considered over the last 15 years. They are listed in a paper I wrote on this subject. Its 80 pages long and pretty boring to read. )

In your convention the equation should read E₀ = mc². I've modified my web page to clarify terms. Have you ever read Rindler's Intro to SR text in your travels?

I also have no idea where you see E = mc² in that page! It does not apply to the mass here so it is not used. I mention energy only to show that matter (where I use the term "matter" as Einstein defined it) is in the box.

I have updated my web page to clarify these things.

Pete

 

[nemosum]

I have another question. In the book "Einstein's Universe" Nigel Calder says that as you approach a center of gravity a little bit of your rest-energy is shed. He makes reference to a certain Roger Penrose (I think) who designed a hypothetical machine which would launch a bucket full of garbage towards a rotating black whole. As the garbage approached, it woud emit large amounts of its rest-energy, which the bucket would absorb in the form of kinetic energy. The bucket would then swing around the black hole (it didn't reach the inner horizen), and come back to the machine, which would turn it's kinetic energy into power by means of a turbine. At least that's how I think it was supposed to go. The problem is that many people have been telling me that being closer to a center of gravity doesn't make your rest-energy less. What am I missing?

 

[jtbell]

An individual elementary particle (such as an electron) can't "shed rest-energy", as far as I know. That would change the rest mass, which is a fundamental property of an elementary particle. I can think of three possibilities:

1. Maybe you misunderstood what Calder wrote.

2. Maybe Calder misunderstood what Penrose wrote.

3. Maybe Penrose was referring to complex objects, i.e. bound systems of elementary particles. The rest mass or rest energy of a complex object does not equal the sum of the rest mass or rest energy of its component particles. It also includes the potential energy that binds the system together, and the kinetic energy of the individual particles relative to the center of mass of the system (for example thermal energy of the atoms in a brick).

 

[daniel_i_l]

Time and Force

I think that this question is relavant to this thread so I didn't want to open another one:
If a force is exerted on a mass in one of the spatial dimensions, then it gets accelerated in that dimension and "deaccelerated" through time. If time is just another dimension then why should a force in one of the spatial dimensions affect the ticking of a clock (time dialation) and not the position in anyone of the other spatial dimensions? Furthermore, let's say that we stop the mass from moving in the spatial dimension, how could that possibly increase the rate of the ticking (speed of time) in the time dimension - there was no force or anything else for that matter in that dimension. I think that the answer has to do with the fact that force causes acceleration and acceleration has to do with time (even more than it has to do with distance - m/s/s), but I wasn't able to see a clear solution. Thanks in advance!

 

[pmb_phy]

"deaccelerated" through time.

What does that mean??

Pete

 

[daniel_i_l]

What does that mean??
Pete

It means that the faster you go through space the slower you move through time, so if you speed through space changes at a nonconsistant rate, so will the rate of your clock, this is what I meant by "deacceleration" through time.

 

[nemosum]

You do understand, don't you, that regarless of your "speed" (which is relative so something which you have left unstated and wherein lies the problem) that if you look at your wristwatch (time-o-meter) it will never run any different. Its workings/rate will always be measured by you to be the same - no matter what your speed is relative to something else.
Pete

Alright, then let's say from now on that the subject object, or person, is flying in our solarsystem, and that it is fairly close to the earth. But for the sake of simpliflying things let's ignore gravitational influence from the sun, and the Earth's orbit around it. In which case we can use the Earth as a point to measure speed etc. by. OK?

And when measuring how fast you "move" (not move as we usually use the word) through time, we will always have to think of it through the eyes of a 2nd person. Because, as you said, you will always observe your clock running normal, and nothing will happen to you energy. But to another person your clock will run slow, and you will have more relativistic mass.

So, assuming we could find a way to measure you "movement" through time, what would be the link between that, and your total energy. Because it seems to me that since you gain energy by moving in the 3 spatial dimensions, something should be the consequence of "moving" through time.
And one last note: can we please establish that the rate at which you "move" through time is 1/time dilation factor (sec.)?

And, how can I get the program to type mathematical symbols?

 

[daniel_i_l]

And, how can I get the program to type mathematical symbols?

Look at the first post in the General Physics section.

 

[daniel_i_l]

So, assuming we could find a way to measure you "movement" through time, what would be the link between that, and your total energy. Because it seems to me that since you gain energy by moving in the 3 spatial dimensions, something should be the consequence of "moving" through time.

Whenever you gain energy by accelerating in the 3 spatial dimensions, you're at the same time moving through time, space and time are intertwined one with another, so any consequence of "moving" through space is also a consequence of "moving" through time.

 

[El Hombre Invisible]

In that case, it's just the time-dilation factor \gamma, or maybe 1/\gamma depending on which way you're looking at it.
To me, the problem with terminology like "moving through time" is that (to me) it seems to imply that there is some kind of absolute time that an object's "motion though time" can be reckoned relative to. But there is no such thing! These different rates of "motion through time" for an object are always observed by different observers, and two different observers in different reference frames observe different rates. The object itself (or an observer riding along with it) always observes its own "motion through time" to be at the same rate.
The problem with using words to discuss stuff like this is that different people tend to associate different things with the same words. Also, if different peole use different sets of words to describe the same things, it gets confusing. I consider terms like "motion through time" to be more like metaphors than terms for practical discussion. I'm pretty sure you won't find it in any real textbook, as opposed to hand-waving popularizations of relativity.

All of this is very true but can equally be said of "moving through space" (there are no absolute x, y, z axes) and indeed the other relative quantities we have been discussing: kinetic energy and mass.

I, within the scope of this discussion, have been defining "moving through time" to the extent that we can compare the rate by which time passes for an observer ( = 1) and the rate by which the observer knows time passes for the subject. In other words, how much of the subject's egg-timer has sifted in the time it takes the observer's to finish.

 

[jackle]

To me, the problem with terminology like "moving through time" is that (to me) it seems to imply that there is some kind of absolute time that an object's "motion though time" can be reckoned relative to.

It is also true that moving through space, there is no absolute space (ether) that you can be reckoned to move relative to. People tend to assume absolute time because time appears that way in every day situations, when in fact, time must be associated with a reference frame. I find "moving through space-time" to be a little better.

Back to the original question, I think there is an energy associated with traveling through time, it is a constant, zero (so we can ignore it). It may be mathematically possible to give it a non-zero value as a function of mass and velocity and subtract that from the equation for kinetic energy, so it is just a part of the kinetic energy. This seems to me like an exercise in making fudge though.

We can in fact split the actual kinetic energy into four components, one that results from motion through space, one that results from motion through time, one given by the fairies and one sent from Aslan. As long as all these components always add up to the actual kinetic energy and as long as they can only be experienced by merit of their contribution to the actual kinetic energy, I'd say the whole thing is blissfully inconsequential.

 

[El Hombre Invisible]

I have another question. In that book the guys says that as you approach a center of gravity a little bit of your rest-energy is shed. He makes reference to a certain Roger Penrose (I think) who designed a hypothetical machine which would launch a bucket full of garbage towards a rotating black whole. As the garbage approached, it woud emit large amounts of its rest-energy, which the bucket would absorb in the form of kinetic energy. The bucket would then swing around the black hole (it didn't reach the inner horizen), and come back to the machine, which would turn it's kinetic energy into power by means of a turbine. At least that's how I think it was supposed to go. The problem is that many people have been telling me that being closer to a center of gravity doesn't make your rest-energy less. What am I missing?

Mechanical energy is the sum of kinetic energy and potential energy. The gravitational potential energy of a body due to another is zero when the distance is infinite, and less than zero at any finite distance. In short, as a body such as a rock falls towards another body such as the Earth, it loses potential energy and gains kinetic energy in equal proportions, hence energy is conserved.

If you now imagine a rock at some height above the Earth at rest. It's mechnical energy at this instance is equal to its potential energy (i.e. negative). If you now take this rock and put it on the surface of the Earth, its kinetic energy is still zero and its potential energy even more negative. So it has less energy than before.

This difference in energy by E = mc^2 yields the mass decrease I think you refer to.

 

[pmb_phy]

It is also true that moving through space, there is no absolute space (ether) that you can be reckoned to move relative to.

Yup. Quite true. This is a frame dependant concept. It is correct to speak of something moving through space if you specify an observer (i.e. coordinate system).

Pete

 

[jtbell]

After reading the comments on "moving through time," the standard spacetime diagram popped into my head: x and ct axes for a particular observer (assuming one spatial dimension for simplicity), with the world line of an object laid out on it. On that world line we mark the the events corresponding to ticks of a clock that is moving along with the object. These ticks of course indicate the object's proper time \tau. I can see that we can equally well talk about dx/d\tau and d(ct)/d\tau.

I guess my discomfort with associating the phrase "moving through time" with d(ct)/d\tau has to do with this: when I think of "moving through space", I normally think of dx/dt, not dx/d\tau.

 

[Mortimer]

I guess my discomfort with associating the phrase "moving through time" with d(ct)/d\tau has to do with this: when I think of "moving through space", I normally think of dx/dt, not dx/d\tau.

In this context, perhaps it is appropriate to refer to my https://www.physicsforums.com/showpost.php?p=805033&postcount=32" in this thread again? (if robphy allows me to )

 

[daniel_i_l]

Can you explain what you mean by time being a "fifth" dimension? I see it in the math but what does it physicly mean?

 

[Mortimer]

Can you explain what you mean by time being a "fifth" dimension? I see it in the math but what does it physicly mean?

Since \tau already takes the obvious role of 4th coordinate in this representation, t itself can no longer be that 4th coordinate. that gives the option to either consider it a parameter (as in a parameterized equation) or (and this is dangerous in terms of being speculative) a real fifth dimension.
Choosing the parameter option leaves you with the uncomfortable question what the heck this parameter is controlled by.
Actually, jtbell already gave his own interpretation of it in:

To me, the problem with terminology like "moving through time" is that (to me) it seems to imply that there is some kind of absolute time that an object's "motion though time" can be reckoned relative to.

The problem with dx/d\tau is that it is a component of the Minkowski 4-velocity vector. This vector cannot be interpreted or treated in the same way as a normal 3-velocity vector where the spatial speed is dx/dt. Also the temporal component of the 4-velocity, dt/d\tau is not a speed in the normal sense.

 

[nemosum]

Could anyone recommend a fairly good book an SR & GR that doesn't require calculus and other advanced math?

 

[masudr]

Could anyone recommend a fairly good book an SR & GR that doesn't require calculus and other advanced math?

There are lots of books on SR and GR without advanced maths, but you probably won't learn much from them. SR, and especially GR, are highly mathematical theories, and you can't expect to really understand them without tough maths (they didn't call Einstein a genius just cos he had fuzzy white hair).

 

[El Hombre Invisible]

Could anyone recommend a fairly good book an SR & GR that doesn't require calculus and other advanced math?

I would recommend 'Relativity' by Albert Einstein.

 

[robphy]

Could anyone recommend a fairly good book an SR & GR that doesn't require calculus and other advanced math?

Geroch, General Relativity from A to B
https://www.amazon.com/gp/product/0226288641/?tag=pfamazon01-20
is a book with very little mathematics. However, don't let that fool you. It is one of the clearest (and unique) presentations of the conceptual structure of special and general relativity. (The chapter on Minkowski Space in his Mathematical Physics book https://www.amazon.com/gp/product/0226288625/?tag=pfamazon01-20 was also quite illuminating for me.) [Admittedly, although I was first introduced to this book as a freshman in college, I didn't fully appreciate it until after taking relativity courses. Looking back, I think I missed the point the first time around because I was looking for the equations seen in textbooks rather than focusing on the conceptual structure, which is not found in your standard textbooks.]

Ellis and Williams, Flat and Curved Space-Times
https://www.amazon.com/gp/product/0198511698/?tag=pfamazon01-20
uses carefully drawn spacetime diagrams to conceptually clarify lots of "relativistic effects". This book requires more mathematical ability. However, one can always skim over those more advanced parts for now.

 

[pmb_phy]

At the moment I'm reading Classical Chared Particles by Fritz Rorhlich. He gets into GR and the basics. He does a supreme job at this. The first chapter on the philosophy of science is the best I've ever read regarding that science an theories are.

Pete

 

[nemosum]

Hey thanks! I'll look these up.

 

[nemosum]

Is there any massless particle that travels in time in it's own frame?

 

[El Hombre Invisible]

Is there any massless particle that travels in time in it's own frame?

Well, this is the difficulty in referring to massless particles: they don't have their own frame. Any massless particle moves at speed c in all frames. When we say that photons "don't travel through time", what we mean is that if you transform the time interval between, say, emission and absorption observed in our frame, however long that may be, to find the time interval in a frame moving with the photon in our frame at speed c, you always get zero (because 1 - v^2/c^2 = 0). But you can't call this frame the photon's 'rest frame'. Same goes for other massless particles.

I would presume that a photon would be red-shifted out of existence in its own frame. Can anyone verify/contradict that?

 

[masudr]

I would recommend 'Relativity' by Albert Einstein.

I wouldn't personally. It's OK but there is more to relativity than Einstein. Besides, he uses outdated notation and mathematical structures that aren't necessarily well suited to the subject. It's been about 90 years since the advent of GR and we have learned a lot since.

Furthermore, this title is OK-ish for the special theory but the general theory is given a very (and necessarily so) light treatment.

 

[nemosum]

Do we know exactly what would happen to an objects rest mass is it reached the speed of light? And does relativistic mass make an object look bigger?

 

[El Hombre Invisible]

Do we know exactly what would happen to an objects rest mass is it reached the speed of light?

Yes, nothing.

And does relativistic mass make an object look bigger?

No, it doesn't.

 

[nemosum]

In another thread someone posted a scenario in which as light-year long wall travels at a certain percentage of the speed of light so that it contracts to 1 foot. If you looked at the wall as it went past would you see it as a foot, or a light-year long?

 

[El Hombre Invisible]

In another thread someone posted a scenario in which as light-year long wall travels at a certain percentage of the speed of light so that it contracts to 1 foot. If you looked at the wall as it went past would you see it as a foot, or a light-year long?

1 foot. Length contraction always occurs in the direction of motion of the moving body, irrespective of the observer's position.