Highschool student interested in cosmology

[heliocentricprose]

I am a high school student interested in cosmology and gr, qm, and mtheory. I find it fascinating to think about the origins of the universe. I need clarification on a 'simple' aspect of the gr theory.

*Time is warped and slowed down (relative to another location) around greater masses
*As objects approach the speed of light, their massess increase, therefore slowing down their 'time'
*If an object is moving at the speed of light, it has a much slower time when compared to something moving at a lesser velocity, in fact, it would appear to the stationary observer that the object moving at lightspeed is not aging at all.

Please correct me if I am wrong.

 

[Severian596]

I am a high school student interested in cosmology and gr, qm, and mtheory. I find it fascinating to think about the origins of the universe. I need clarification on a 'simple' aspect of the gr theory.

*Time is warped and slowed down (relative to another location) around greater masses
*As objects approach the speed of light, their massess increase, therefore slowing down their 'time'
*If an object is moving at the speed of light, it has a much slower time when compared to something moving at a lesser velocity, in fact, it would appear to the stationary observer that the object moving at lightspeed is not aging at all.

Please correct me if I am wrong.

Hi heliocentricprose, welcome to the boards. You're diving right in, aren't you!?

If you'd like to discuss "simple" aspects of the General Theory, why not discuss Special Relativity instead? (The second) two points you asked about are relevant questions in SR. However since SR assumes no gravity, the first question is not relevant. But anyway, I'll answer some things as best I can for you, then check out Wikipedia for some really, really interesting and compelling info, okay? Furthermore, understand that General Relativity is considerably more complex than SR, especially in math. SR can be understood with High School algebra, but not GR. However, feel free to look up GR in wikipedia for narrative info, too.

Then look up Pete's awesome pages that illustrate the math behind SR! Pete (pmb_phy in these forums) really did a great job with these, and he helped me learn the topic.
http://www.geocities.com/physics_world/sr/sr.htm

*As objects approach the speed of light, their massess increase, therefore slowing down their 'time'
The two ideas are not really related to each other, but you've got the basic idea. As an object approaches the speed of light (SL) its mass increases. This is why massive objects cannot achieve the speed of light...eventually it would take infinite energy to accelerate even one massive particle to the speed c. But this does not cause anything funky with the particle's time.

Time changes are relative. Each of us experiences time in our own surroundings (frame of reference or reference frame) the same way. No matter what our speed is, time in our reference frame will feel "normal." Remember this! It's the most important fact and the fact that most people new to the topic get confused. Two observers who are moving relative to each other will therefore notice two things:
1) Time for them feels normal (remember, I said that)
2) Time for the other guy happens slower

Remember these two things and you won't go wrong as you continue your research! Don't forget them. Both think the other person's clock ticks slower...

*If an object is moving at the speed of light, it has a much slower time when compared to something moving at a lesser velocity, in fact, it would appear to the stationary observer that the object moving at lightspeed is not aging at all.
Yep! Nicely said. Remember points 1 & 2 from my previous response...it applies here, too. Then you'll learn that a photon thinks nothing ages anywhere...at all. The photon goes wherever it wants in zero time as far as its concerned. If it could think, anyway.

 

[heliocentricprose]

thanks, it really helps

so, am i correct in deducing that
*Everything moves through 4-dimensional spacetime at the speed of light, the faster the speed, the slower time (to a stationary observer).

 

[pervect]

thanks, it really helps

so, am i correct in deducing that
*Everything moves through 4-dimensional spacetime at the speed of light, the faster the speed, the slower time (to a stationary observer).

You'll probably get a lot of negative comments on that particular phrasing, because while motion through space is well defined, motion through space-time isn't.

You appear to be trying to say that in special relativity (SR), the 4-velocity of any object has an invariant magnitude equal to the speed of light, which is a true statement.

 

[Garth]

thanks, it really helps

so, am i correct in deducing that
*Everything moves through 4-dimensional spacetime at the speed of light, the faster the speed, the slower time (to a stationary observer).

HI heliocentricprose!

As pervect said that question does not really make sense as nothing 'moves' in space-time. Movement requires the passsage of time and time is already accounted for in space-time!

However everything does have a 4-velocity, not
$$v = \frac{dx}{dt}$$,

which is ordinary velocity through 3D space, but

$$v^\mu = \frac{dx^/mu}{d\tau}$$,

where $x^\mu$ is the coordinate in the $\mu$ dimension (including $\mu = 0 : t$ and $\tau$ is the proper time given by the metric:

$$d\tau^2 = dt^2 - \frac{1}{c^2}(dx^2 + dy^2 + dz^2)$$

in SR flat space-time.

It works out that the magnitude or norm of the 4-velocity of any particle is always the same as the speed of light, so you might want to say that we 'move' through space-time at one 'second' per 'second', if you understand what you mean by that statement!

(In space-time to get the dimensionality correct you have to convert the space dimensions into time dimensions (one metre ~ one second/300,000,000), or the time dimension into a space dimension (one second ~ 300,000,000 metres) the speed of light is then unity (one second per second))

I hope this helps.

Garth

 

[robphy]

However, note that zero-mass objects (like photons) don't have [unit] 4-velocities since the tangent vectors to their worldlines have zero norm. In this case, their 3-velocities have magnitude of "the speed of light".

 

[heliocentricprose]

Are photons zero-mass objects?
I thought they at least have some miniscule mass due to the warping of light around a massive object, say... the sun. They are affected by gravitational fields afterall.

Thanks for the replies. It clarified a lot. So the 4-velocities of all objects are the same, which gives rise to another question. To measure speed, you need two objects. Both are initially the same mass. One is the 'stationary' object, and the other is moving away from it with some velocity. The speed of light is an absolute number; it does not change. One of the objects is moving closer to the speed of light than the other. Obviously, this object has a greater mass because of its greater velocity. But, if the object moving closer to the speed of light is the observer, it would appear that the other object is moving away, closer to the speed of light. Is this a paradox? Is mass just as relative as time?

I don't really understand what Garth said:
"(In space-time to get the dimensionality correct you have to convert the space dimensions into time dimensions (one metre ~ one second/300,000,000), or the time dimension into a space dimension (one second ~ 300,000,000 metres) the speed of light is then unity (one second per second))"

It seems to me that you're saying that time can be converted into space, which boggles my mind.

 

[Garth]

You have to convert units to keep the dimensionality correct.

If you had dollars and euros, and wanted to know how much in total you had, you would use an exchange rate to convert the euros into dollars, or the other way round, so you could say: "I have so many dollars, or euros, worth of money."

Here the 'exchange rate' between space and time is a velocity, multiply a time by a velocity and you get a distance, divide a distance by a velocity and you get a time.

We call that velocity "c", and you can show that if space and time are linked by the SR metric, my post #5 above, then a massless photon has to travel through a vacuum at that velocity c, so c is identified as the velocity of light, ~ 300,000,000 m.sec^-1.

And yes, photons are massless objects, they have momentum and energy but not (rest) mass.

Also, because of the time dilation effect, when one observer observes another moving relative to her, then all observers measure the velocity of light to be the same, c. It is not a paradox. The velocity of light is one of the invariants of nature, proper time, $\tau$, being another.

I hope this helps,

Garth

 

[Ratzinger]

-photon have no mass, light bending happens because spacetime is bend and light is just following the shortest paths in this curved spacetime ( according to Einsteins general relativity)

-the norm of all four-velocities is the same

-space and time are distinct things, but you can measure them with same units, lightseconds for example, so one second correspond to 300000km

 

[Severian596]

One of the objects is moving closer to the speed of light than the other. Obviously, this object has a greater mass because of its greater velocity. But, if the object moving closer to the speed of light is the observer, it would appear that the other object is moving away, closer to the speed of light. Is this a paradox?

It's not a paradox...a paradox, shamelessly copied from Wikipedia, is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition. Really what you've described is simply relativity itself.