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View Full Version : Can I put planet Earth in my pocket - and if so how heavy would it be ?

Phobos
2010-Sep-08, 10:07 PM
At first the answer to this one would seem obvious ... shrink it down to it's minimal size (the size of a pea) so that it becomes a mini black hole. If you were abe to put it in your pocket it would have the same mass, and would therefore still weigh the same. But I am interested in discussing a slightly more esoteric aproach to this problem.

If we examine M theory it suggests the our universe is actually 11 dimensional in aspect. Whilst string theory only suggests 10 dimensions, M theory adds one extra dimension ... and this introduces the idea of membrane universes as the dimension is a 4th spacial dimension.

My thought experiment works like this. If we were able to move along this 4th spacial dimension and discover that our planet is actually a 4 dimensional hypersphere (something that has been suggested) then our observation of our planet would be somewhat strange - it would appear to shrink.

Following this principle to the extreme, a journey along a fourth spacial dimension would (provided our planet is a hypersphere) result in our planet reaching a point whereby it eventually reaches a very small size indeed.

So the question arises, if our planet could shrink in this manner (from our perspective) then how much would it weigh ?

Canis Lupus
2010-Sep-08, 10:37 PM
Wouldn't Earth's weight in your thought experiment be the same as it is now, which has been estimated to be approximately 6,000,000,000,000 ,000,000,000,000 kilograms (http://www.universetoday.com/72928/step-on-the-scales-weighing-up-planet-earth/)?

Despite our collective need to lose weight, Mother Earth seems to be putting on weight gradually, much like myself regrettably. Even worse, infinitesimally, Earth appears to be contributing to my weight gain with its own. :wall:

Phobos
2010-Sep-08, 10:55 PM
Perhaps I need to expain better. Planet Earth's mass won't be affected by an observer being displaced in the 4th spacial dimension, but I am referring to the gravitational attraction of our planet on the observer who travells along this 4th spacial axis. The concept of variance of radius of a hypershere has been around for a very long time and is akin to the changes of radius of horizontal cross sections of a hill as you gain altitude. The bottom line is if our planet is a four dimensional hypersphere then it stands to reason that as we move along the fourth spacial dimension the apparent size of our planet would eventually drop to zero.

What is not clear is would the gravitational attraction to the observer of this body change in proportion to it's apparent size to the observer?

Canis Lupus
2010-Sep-08, 10:59 PM
Yep. after the first paragraph of your OP, you lost me.:confused:

I'll be interested to read more intelligent replies though.

Jens
2010-Sep-09, 05:25 AM
Following this principle to the extreme, a journey along a fourth spacial dimension would (provided our planet is a hypersphere) result in our planet reaching a point whereby it eventually reaches a very small size indeed.

So the question arises, if our planet could shrink in this manner (from our perspective) then how much would it weigh ?

I'm not sure if I quite get it, but I think I understand. If so, can't you ask the same question with other dimensions? If you move along say the height dimension, so that you're moving above the north pole, the earth will gradually shrink in size, and its mass will remain identical but you would feel it decreasing as an inverse-square of distance. So wouldn't the same thing happen with the hypothetical fourth dimension? As you move away from the earth in the fourth dimension, it will get smaller and its gravitational attraction will decrease?

Phobos
2010-Sep-09, 07:24 AM
If there is a fourth spacial dimension it iis very different from the other 3 we are familiar with. The 3 we are all familiar with extend in our universe for immense distances (although probably not infinate - we can assume this as the big bang would suggest a non-infinate universe in 3 dimensions). If M theory is correct the fourth spacial dimension is less than one millimetre in totallity.

In M theory, our 3D universe is presented as a "membrane" universe - just one in a stack of universes which are collectively known as a multiverse. That said four dimensional shapes are by no means new to theoretical mathematics and it's here where the ideas of what happens to a 4d hypersphere as you travel through a fourth dimension come from.

caveman1917
2010-Sep-10, 12:57 AM
If there is a fourth spacial dimension it iis very different from the other 3 we are familiar with. The 3 we are all familiar with extend in our universe for immense distances (although probably not infinate - we can assume this as the big bang would suggest a non-infinate universe in 3 dimensions). If M theory is correct the fourth spacial dimension is less than one millimetre in totallity.

In M theory, our 3D universe is presented as a "membrane" universe - just one in a stack of universes which are collectively known as a multiverse. That said four dimensional shapes are by no means new to theoretical mathematics and it's here where the ideas of what happens to a 4d hypersphere as you travel through a fourth dimension come from.

If your 4th dimension is only about a millimeter in size, how could you get further from earth than a millimeter through it?

I'm not sure what you claim is indeed what M-theory says. Could you provide a reference please?
As far as i know brane theory is the alternative to the standard "curled up" (calabi-yau) dimensions.

Ivan Viehoff
2010-Sep-15, 03:12 PM
"When Witten named M-theory, he did not specify what the "M" stood for, presumably because he did not feel he had the right to name a theory which he had not been able to fully describe." (Wikipedia) M-theory, like string theory, remains an aspiration rather than a theory that can be applied or tested. So far it doesn't make any predictions about anything. So I think thought experiments about what it might predict lies more in the realm of science fiction than science and technology.

EDG
2010-Sep-16, 03:31 AM
M-theory, like string theory, remains an aspiration rather than a theory that can be applied or tested. So far it doesn't make any predictions about anything. So I think thought experiments about what it might predict lies more in the realm of science fiction than science and technology.

Also from wikipedia: http://en.wikipedia.org/wiki/String_theory#Problems_and_controversy

It seems that there are actually several predictions that can be made, and ways that String Theory can be falsified. It's one thing to be unconvinced by it, but it seems to me that some people are intent on misrepresenting its capabilities (for reasons unclear to me).

Ivan Viehoff
2010-Sep-16, 10:30 AM
Also from wikipedia: http://en.wikipedia.org/wiki/String_theory#Problems_and_controversy
It seems that there are actually several predictions that can be made, and ways that String Theory can be falsified.
That seems to be a summary of my understanding of the state of affairs. The standard model is in effect embedded in string theory (or the 10^500 theories - according to one estimate - that may be embodied by the collective term "string theory"). There's no power in string theory unless it makes a testable prediction beyond the standard model. A prediction testable at 10^14 times the energy of the LHC suggests that the power of the theory isn't quite nothing, but very close to it: in other words, it doesn't really tell us, in a scientific sense, anything we didn't already know within the range of things that we can measure.

And that's string theory. M-theory is an incomplete theory beyond that.

So, we have few if any predictions of any use made by String/M theory beyond what the standard model already predicts. Therefore OP's thought experiment of whether String/M theory might predict X doesn't seem likely to go anywhere.

"String theory makes a testable prediction" headlines come out about once a month these days. So far they have all turned out to be nonsense, and are actually counter-productive as they make string theorists look desperate.

Phobos
2012-Feb-02, 01:40 AM
It's a little late tonight but I will get back to this. For now you will find the following link covers most of what I have been talking about;

http://lofi.forum.physorg.com/That-10th-Spatial-Dimension-Of-M-Theory_23159.html

I should add that hyperspheres are purely theoretical, and we currently have no idea how we could travel along the fourth spacial dimension (if it does indeed exist).

Trebuchet
2012-Feb-02, 04:00 PM
Well, that's a strange page. Love how the text keeps getting smaller all the way down!

I can put Planet Earth (http://www.amazon.com/Planet-Earth-Six-Disc-Special-Blu-ray/dp/B005C9YZIW/ref=sr_1_1?ie=UTF8&qid=1328198407&sr=8-1) in a moderately large pocket. It weighs only a few ounces.