Exploring Time Dilation and Mass

[aglo6509]

Hello,
I don't know if this is the right place to come for my type of question but its the place that made sense to me so here it goes.

I know that time stretches out when traveling near c (I am familiar with Einstein's twin paradox), however I remember somewhere I heard that objects with a large mass "drags" through time. The only visual I can give myself is to picture time as a fabric and when, for example, a human is placed on this "fabric" some drag happens but not so much. Now I picture putting a pyramid on this "fabric" and now compared to the "drag" from the human this "drag" is far more extreme.

I guess I'm basically asking is my idea that more mass is traveling "slower" in time when compared to a mass significantly smaller to it?

 

[ZealScience]

I can't thoroughly understand, but if you really look at the Lorentz transformation equations, you will see that the time dilation is independent of mass. The time dilation only depends on the speed.

Another Lorentz Transformation, the transformation of mass is basically gain in kinetic and thus gain in equivalent mass. Youshould read more on that.

 

[henry_m]

You may be referring to the phenomenon of "frame-dragging", but this is a gravitational effect and not really the same thing as time dilation and twin paradox type scenarios.

The idea of the effect is that something in motion sort of "drags" spacetime round with it. One example of this is a massive rotating object, like the earth. According to Newtonian gravity, the gravitational field doesn't depend at all on this rotation, and this is a very good approximation. But according to general relativity, the rotation of the planet causes a slight 'twisting' of spacetime. An example of a physical effect of this: imagine putting accurate synchronised clocks on a pair of satellites, before setting them off in opposite directions at equal speeds around the earth. Once they have completed an orbit and returned to the point where they started, you collect them and look at the clocks. You find that the one orbiting in the same direction as the rotation of the Earth has recorded less time! This sort of effect has been measured by the satellite experiment Gravity Probe B.

 

[ZealScience]

If you mean the curvature of space time, it is caused by the inner part of the curvature of space time is "shorter" than that of the outer.

Mathematically ,curvature is greater when an surface is more bent (obviously), so it depends on the mass which generates the curvature. I think black hole is a good example, where time is extremely dialated.

In my perspective, the Fabric you said is a good analogy to what it is in Minkovsky coordinate system, but geometry is the same.

 

[aglo6509]

Those are some very interesting ideas, thank you for telling me them. I wish I had more mathematics under my belt to understand the Lorentz transformation equations (I just finished Calculus 2). I remember that from that source I heard this information from, I still can't think of its name, it was saying if you were to stand next to a pyramid you would age slower then someone who wants standing next to. Granted however that you would only age slower by a very tiny bit, but still slower.

 

[henry_m]

... if you were to stand next to a pyramid you would age slower then someone who wants standing next to. Granted however that you would only age slower by a very tiny bit, but still slower.

Ah, that's another different effect again, usually referred to as 'gravitational redshift'. A clock in a strong gravitational field will run slower than a clock in a weaker field. Some large mass, like your pyramid, will create a very slightly larger gravitational field so that's where the effect you describe comes from. That example would be so tiny as to be virtually impossible to measure, I'd have thought, but the effect can actually be significant enough in some circumstances to be important from a practical point of view! The shift has to be taken into account on the clocks in GPS satellites, which require very accurate timing.

Unfortunately, the mathematics needed to describe general relativity is quite advanced, but you can still understand why it should be true from a more heuristic point of view. I'll post a bit more on this when I have a bit more time.

 

[nitsuj]

I guess I'm basically asking is my idea that more mass is traveling "slower" in time when compared to a mass significantly smaller to it?

yea for sure, time clicks slower on Earth compared to the GPS satilites way up high.

earth gravity is strongest around the surface I think. I guess time clicks faster in the centre of Earth too.

 

[aglo6509]

Ah, that's another different effect again, usually referred to as 'gravitational redshift'. A clock in a strong gravitational field will run slower than a clock in a weaker field. Some large mass, like your pyramid, will create a very slightly larger gravitational field so that's where the effect you describe comes from. That example would be so tiny as to be virtually impossible to measure, I'd have thought, but the effect can actually be significant enough in some circumstances to be important from a practical point of view! The shift has to be taken into account on the clocks in GPS satellites, which require very accurate timing.

Unfortunately, the mathematics needed to describe general relativity is quite advanced, but you can still understand why it should be true from a more heuristic point of view. I'll post a bit more on this when I have a bit more time.

Oh I read in a book called "Cracking the Einstein Code" about redshifts. Due to my low level of physics courses, just physics 1 and 2, I haven't seen much of these topics. So understanding redshift was hard for me and I still don't really know much about it. I can't wait until I get into those high level Physics/Math course. Also I'm excited to read more about this from you

 

[ZealScience]

Ah, that's another different effect again, usually referred to as 'gravitational redshift'. A clock in a strong gravitational field will run slower than a clock in a weaker field. Some large mass, like your pyramid, will create a very slightly larger gravitational field so that's where the effect you describe comes from. That example would be so tiny as to be virtually impossible to measure, I'd have thought, but the effect can actually be significant enough in some circumstances to be important from a practical point of view! The shift has to be taken into account on the clocks in GPS satellites, which require very accurate timing.

Unfortunately, the mathematics needed to describe general relativity is quite advanced, but you can still understand why it should be true from a more heuristic point of view. I'll post a bit more on this when I have a bit more time.

Agreed. When object approaches the event horizon it will seems redder and redder and finally shift to infra red and disappears. Just like what I said, time drag depends on the curvature of the space. At the sigularity point of the black hole curvature approaches infinity, but at the event horizon, curvature is much smaller, so the time shift difference is great. But a pyramid has a low density comparing to black holes and too "light" to generate such a curvature. That's what I understand. I think you should look more on topic like curvature of space time.

Though it requires a little bit linear algebra to describe the Minkovsky coordinate system, but to understand curvature, calculus is sufficient. You can look parallel transport in defining curvature.

 

[aglo6509]

Though it requires a little bit linear algebra to describe the Minkovsky coordinate system, but to understand curvature, calculus is sufficient. You can look parallel transport in defining curvature.

Do you have any recommendations on some reading material in such area?

 

[ZealScience]

Do you have any recommendations on some reading material in such area?

Sorry I am not expert just of great interest in physics, but I can tell you about some topics:

Anything involving tensor computation is very important in general relativity as well as linear mapping (often used as a commutor between coordinates like covariance contravariance).

I don't know whether your calculus 2 contains partial differentiation? It plays a great part in coordinate transformation.

To know about curvature you must learn about parallel transport which defines curvature

http://en.wikipedia.org/wiki/Parallel_transport
http://en.wikipedia.org/wiki/Curvature

That's all what I know

In addition open courses from Stanford can be handy. I've been watching that, really good program.

 

[aglo6509]

Sorry I am not expert just of great interest in physics, but I can tell you about some topics:

Anything involving tensor computation is very important in general relativity as well as linear mapping (often used as a commutor between coordinates like covariance contravariance).

I don't know whether your calculus 2 contains partial differentiation? It plays a great part in coordinate transformation.

To know about curvature you must learn about parallel transport which defines curvature

http://en.wikipedia.org/wiki/Parallel_transport
http://en.wikipedia.org/wiki/Curvature

That's all what I know

In addition open courses from Stanford can be handy. I've been watching that, really good program.

No, sadly my calculus 2 didn't cover p-derivatives. I did however look it up on youtube so I'm vaguely familiar with it. The Stanford open courses are nice, also MIT has some with Professor Lewin, they're also great.

 

[PAllen]

Ah, that's another different effect again, usually referred to as 'gravitational redshift'. A clock in a strong gravitational field will run slower than a clock in a weaker field. Some large mass, like your pyramid, will create a very slightly larger gravitational field so that's where the effect you describe comes from. That example would be so tiny as to be virtually impossible to measure, I'd have thought, but the effect can actually be significant enough in some circumstances to be important from a practical point of view! The shift has to be taken into account on the clocks in GPS satellites, which require very accurate timing.

Unfortunately, the mathematics needed to describe general relativity is quite advanced, but you can still understand why it should be true from a more heuristic point of view. I'll post a bit more on this when I have a bit more time.

The very latest experimental clocks are so sensitive that they detect the difference in time flow between the top of a table and the floor below it (let alone differences between any two cities). It seems to me they are so sensitive they add no value as standard clocks because there is no plausible way to pick a standard; but they are very useful to detect the tiniest differences in time flow.

 

[aglo6509]

So if time varies with everything, even to the smallest amount, there is no "standard time". Time is only the same for the observer?

 

[ZealScience]

So if time varies with everything, even to the smallest amount, there is no "standard time". Time is only the same for the observer?

Yes, exactly. Because simultaneity is meaningless to relativity, which means exactly taht there is no such thing as a "standard time", to my understanding

 

[aglo6509]

Yes, exactly. Because simultaneity is meaningless to relativity, which means exactly taht there is no such thing as a "standard time", to my understanding

And this is caused by everything having its own curvature in spacetime, or is that only for massive objects, like the earth?

 

[ZealScience]

And this is caused by everything having its own curvature in spacetime, or is that only for massive objects, like the earth?

I think it is the basic idea from special relativity, it's simply about reference frames, different reference frames observe with different time frame. Time can vary with, for example, Lorentz transformation. Standard time, I guess, comes from Newton's space AND time, which is definate, but in relativity space time is one thing that varies together.

I haven't gone deep into it, either, I'm also learning it. I hope you can understand it after you finish your Special Relativity course.

 

[aglo6509]

I haven't gone deep into it, either, I'm also learning it. I hope you can understand it after you finish your Special Relativity course.

I'm only going in intro physics 3 I can't wait until I get into the really cool stuff!

 

[ZealScience]

I'm only going in intro physics 3 I can't wait until I get into the really cool stuff!

You can read the novel The New World of Mr Tompkins by Gamow (Physicist renowed for Big Bang Theory and the books). It is not a professional book, but it describes relativity so vividly that even Grandma Can Understand! It really gives you a good insight about relativity. It provide also some basic mathematical ideas from both relativity and quantum (I like quantum more), that you might be interested in.

http://en.wikipedia.org/wiki/Mr_Tompkins

 

[aglo6509]

You can read the novel The New World of Mr Tompkins by Gamow (Physicist renowed for Big Bang Theory and the books). It is not a professional book, but it describes relativity so vividly that even Grandma Can Understand! It really gives you a good insight about relativity. It provide also some basic mathematical ideas from both relativity and quantum (I like quantum more), that you might be interested in.

http://en.wikipedia.org/wiki/Mr_Tompkins

I'll definitely have to check it out, I'm planning on getting a Kindle soon and I checked Amazon and they have it on ebook! I'm a sucker for books that use some of the complex physical ideas and condense it to such laymen terms.

 

[ZealScience]

Hope you enjoy it!

 

[aglo6509]

I'm sure I will, thanks for letting me know such book exists.