Physics Questions: Exploring Special & General Relativity

[human83]

Hi everyone!
I'm really sorry to bother you with my surely stupid questions, but I am 13 years old and today I read some lines about Special Relativity and General Relativity at school and found myself stuck on some thoughts I can't cease to think about... I really hope that you will be so kind to help me, because I'm not clever enough to solve these things out by myself.

(1) I read that every object which has mass curves space-time (though maybe just infinitesimally). (a) Is it right? (b) Does energy (which I think is massless) curve space-time too in the same way? (c) it seems to me that everything which exists alterates space-time in some way... if we can calculate the space-time metric starting from the properties of an object, can we deduce the properties of an object knowing the metric of the region of space-time it occupies? (d) is it legitimate to suppose a complete identity between objects and the regions of space-times they occupy? (e) if I remove all the objects in the universe, does space-time continue to exist? (f) what is exactly a "frame of reference"??

(2) I read about time dilation, length contraction and mass increase. I imagine a spaceship, 1 km long say, which is traveling at a speed where relativistic effects are manifest. (a) why does time slow down in the spaceship? (b) the length contraction of the spaceship is a "real" phenomenon (the ship is really shorter while traveling than when it was orbiting around Earth) or simply an optical effect seen by an observer outside (of the frame of reference) the ship?

(3) Consider again the starship above and suppose that there are two men, one in the bow of the ship and one in the stern of the ship. They both have a nuclear clock (that's to say a really precise clock) which have been perfectly synchronized (if it is possible). (a) Will they find a difference of time between them (though a small one) after a certain period of time though they are on the same spaceship? (b) is there a formula to calculate this difference of time? ('cause I would like to make some calculations on different scenarios)

(4) I read that relativistic effects become significat only near the speed of light. This means that there are relativistic effects at any speed but they are irrelevant and/or undetectable or that they just don't happen (don't exist) below certain speeds? I was thinking about the most stupid experiment in history: suppose we have a huge platform, 100,000 km long (or more if needed) and 20,000 km wide, with a mass of 1,000 kg. At each of the two ends of the platform we put a clock capable of measuring even the smallest interval of time (Planck time I think). The platform is stationary in space. (a) After a period of time (arbitrarily long), am I going to detect a tiny, infinitesimal difference in the time measured by the two clocks? (b) if so, which is the formula I might use to calculate that difference?

I know I am really stupid and ignorant, and I apologize if I'm wasting your time with these questions which are probably really trivial for you... but, as I told you, I am 13 and since I know nothing about physics I thought to ask here instead of killing my curiosity. I also apologize for my terrible English... I'm from Switzerland :)
Thanks for having had the patience to read my silly questions and thanks in advance to those who will have the kindness to descend to my level and help me understand. Thank you very much!

 

[Nabeshin]

Hi everyone!
I'm really sorry to bother you with my surely stupid questions, but I am 13 years old and today I read some lines about Special Relativity and General Relativity at school and found myself stuck on some thoughts I can't cease to think about... I really hope that you will be so kind to help me, because I'm not clever enough to solve these things out by myself.

Hi and welcome to PF! Impressive questions for a thirteen year old!

Let's see...

(1) I read that every object which has mass curves space-time (though maybe just infinitesimally). (a) Is it right? (b) Does energy (which I think is massless) curve space-time too in the same way?

These are both correct. Mass and energy both contribute to the warping of spacetime, but so do less obvious things such as pressure, shearing, and momentum!

(c) it seems to me that everything which exists alterates space-time in some way... if we can calculate the space-time metric starting from the properties of an object, can we deduce the properties of an object knowing the metric of the region of space-time it occupies?

Yes! To understand this, one must understand Einstein's equations. Now, these equations are quite complicated but can actually be written in an extremely compact way:
G=T
(Ignoring some factors of pi).
G is related to the curvature of your spacetime surface and T is related to the mass/energy/momentum distribution. Now, normally we think about the equation in the order I wrote it, G=T, implying (just by normal maths conventions) that the curvature of a surface is a function of the mass/energy distribution. With this approach, we know what the mass distribution is (say, the earth) and we can calculate what spacetime looks like around it. However, we could equally well go the other way and say T=G! That is, if we knew what spacetime looked like, we could deduce the mass/energy/momentum distribution! Spacetime might seem like a strange thing to measure, but if we imagine shooting a bunch of little particles out, their motion will tell us about the curvature of spacetime!

It is important to note though that all the information you will get from this procedure is the mass/energy/momentum/etc. distribution. I.e. you will not be able to tell if a ball causing a gravitational field is red, blue, or polka dot colored.

(d) is it legitimate to suppose a complete identity between objects and the regions of space-times they occupy?

As I've said, different objects can create the same spacetime curvature, so it doesn't make sense to identify specific objects with geometries.

(e) if I remove all the objects in the universe, does space-time continue to exist?

This is a rather philosophical question, akin to 'if a tree falls in a forest...'. As such, I don't really think it's important to dwell on here.

(f) what is exactly a "frame of reference"??

A frame of reference is simply the coordinate system attached to a particular observer. So I, sitting here in my computer chair, can set up a coordinate system and measure the positions of various objects and the durations between events. Similarly, someone running past me has their own reference frame (in which they are stationary!) and can perform the same measurements.

There are some nuances here, but I think for most cases the above understanding is sufficient.

(2) I read about time dilation, length contraction and mass increase. I imagine a spaceship, 1 km long say, which is traveling at a speed where relativistic effects are manifest. (a) why does time slow down in the spaceship?

The short answer is because light must move at the same speed in all reference frames. The way I generally think about it is in accord with the explanation given on wikipedia:
http://en.wikipedia.org/wiki/Time_d...nce_of_time_dilation_due_to_relative_velocity

(b) the length contraction of the spaceship is a "real" phenomenon (the ship is really shorter while traveling than when it was orbiting around Earth) or simply an optical effect seen by an observer outside (of the frame of reference) the ship?

Length contraction certainly is 'real', in that it is not merely an optical illusion. I'm not entirely sure what is meant by 'real' here though.

(3) Consider again the starship above and suppose that there are two men, one in the bow of the ship and one in the stern of the ship. They both have a nuclear clock (that's to say a really precise clock) which have been perfectly synchronized (if it is possible). (a) Will they find a difference of time between them (though a small one) after a certain period of time though they are on the same spaceship? (b) is there a formula to calculate this difference of time? ('cause I would like to make some calculations on different scenarios)

No! There will be no difference in the clocks of these two men. In their reference frame, neither of them is moving, and as such neither is subject to time dilation effects of special relativity.
We can consider the more complicated case of an accelerating spaceship though. One of Einstein's motivations for general relativity was the equivalence principle, which stated simply is the notion that a gravitational field is indistinguishable from an accelerating reference frame on small enough length and time scales. If you imagine sitting in a box on the surface of the Earth, you will feel a force pulling you downwards with precisely the normal gravitational force on the earth. Now, imagine that you are in the same box, but far away from any gravitational source, but instead you have attached rocket boosters to the box and are firing them so as to accelerate at one Earth gravity. Again, you will feel a force pulling you downwards, and assuming the box has no windows or anything, you will be unable to tell whether you are in a box on the Earth or a box in the middle of nowhere!
So just as a clock slows down in a gravitational field (well, a gravitational potential ;), a clock will similarly slow down in an accelerating rocket ship!
To return to the spaceship, even if it is accelerating the two men will not notice a change in their clocks! This is because they are both accelerating at precisely the same rate. Well that's curious.. by the equivalence principle, imagine the rocket to be just sitting on the launch pad on Earth. Well, the guy at one end of the ship will be higher up than the other, the gravitational force on him will be less! As such, his clock will run at a slightly faster rate than the man in the lower part of the ship! Have we broken the equivalence principle?! Not really.
The curious statement 'on small enough length and time scales' appeared in the equivalence principle. This is precisely to handle the case above. In the event that a gravitational field is non-uniform, the equivalence principle no longer holds! So, what we do is we zoom in on a really small space over which the gravitational field is approximately uniform, and again we recover the equivalence.
Just as a note while I'm on the subject, the experiment of putting a clock higher up in a gravitational field and one lower down has been performed and is known as the Pound-Rebka experiment after the scientists who first conducted it in 1959. They had clocks on different stories of a building, but we can now measure the variation in the rate of a clock between basically the bottom and top of your desk!

(4) I read that relativistic effects become significat only near the speed of light. This means that there are relativistic effects at any speed but they are irrelevant and/or undetectable or that they just don't happen (don't exist) below certain speeds? I was thinking about the most stupid experiment in history: suppose we have a huge platform, 100,000 km long (or more if needed) and 20,000 km wide, with a mass of 1,000 kg. At each of the two ends of the platform we put a clock capable of measuring even the smallest interval of time (Planck time I think). The platform is stationary in space. (a) After a period of time (arbitrarily long), am I going to detect a tiny, infinitesimal difference in the time measured by the two clocks? (b) if so, which is the formula I might use to calculate that difference?

Yes indeed relativistic effects are only important at high speeds. The relevant parameter for relativistic effects is known as the lorentz factor:
$$\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$$
Where v is the velocity you're moving at and c is the speed of light. If you plug in some velocities you'll see that for normal speeds, this is ridiculously close to one. Things begin to get relativistic when it deviates significantly from one. As the velocity approaches c, this goes to infinity!
With regards to your very large platform, again there would be no time difference measured. The clocks are attached to the same rigid object and are thus moving with the same velocity.

Phew. That was a bit longer than I expected! Let me know if anything doesn't make sense or if you have more questions!

 

[phinds]

One thing I would add to the above (which is quite a good set of answers) is that time dilation is very weird in one way and that is that the person who travels very fast and comes back has aged less than the person who stayed home BUT to him it did not SEEM as though time was any different than normal. You can read all about this if you google "the twin paradox"

 

[human83]

Nabeshin, I feel I owe you a lot for the time you spent answering my question, the plain language you used, the knowledge you kindly shared, and the kindness you used to me not making me feeling a complete idiot :) Thank you very much, really. I think I will ruminate a lot on your clear explanations but I'm really happy you corrected many of my terrible misunderstatements and mistakes. Please, consider to become a teacher one day, you would be a wonderful one! :)
Thanks also to you Phinds, I vaguely heard about "The twin paradox" but didn't know anything about. It seems a really weird and intriguing phenomenon I would like to study!
Again... Thank you both!

 

[Quinzio]

Well, you should definitely stop to label your questions as stupid or idiot. It's quite impressive a 13 yo boy is managing to explore the details of an unusual and unfamiliar theory such as relativity, although I remember when I was 15 I was already reading some heavy stuff like Bertrand Russel's books. :)
In addition it's remarkable that you are able to write in a good English, given you are in Switzerland and as far as I know, they speak German, French and Italian there, but not English. I've got 3 times your age and I still struggle to improve my English. I'm italian and I've been sometimes to Svizzera.Coming to your questions:
(2) I read about time dilation, length contraction and mass increase. I imagine a spaceship, 1 km long say, which is traveling at a speed where relativistic effects are manifest. (a) why does time slow down in the spaceship? (b) the length contraction of the spaceship is a "real" phenomenon (the ship is really shorter while traveling than when it was orbiting around Earth) or simply an optical effect seen by an observer outside (of the frame of reference) the ship?

To point a) you should look at stuff like this: which explains concepts in a relatively easy way.

As for point b), yes, length contraction is "really" real, although no one will ever experience it. Only experiments and distant measures can reveal it, and as far as I know, no experiment has measured it yet. More food for your thoughts: http://en.wikipedia.org/wiki/Ladder_paradoxGreetings

 

[yoron]

Very sweet thinking human :)

And interesting answers, I would just like to add one thing. When it comes to measuring something in a uniform motion, like with clocks, there will always be a local 'gravity'. As long as we are discussing something of mass at least. And testing atomic clocks on Earth it has been shown that they will show a difference relative gravity, even at so small scales as a meter.

And so I will assume that if we had really precise 'perfect clocks' the approximate 'length of difference' between two points should be somewhere around a Planck length, as a guess and based on our definitions of Planck time 'c' and Plank length. Theoretically we ignore invariant mass in a uniform motion, assuming 'point particles' or infinitely small 'flat' patches in SR as I see it, but in reality, I don't think we can ignore 'gravity' anywhere.

And that makes another definition of what a 'frame of reference' could be seen as.