Gaining Kinetic Energy Through Time: Explained

[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.