Warping Space-time

[hawksmere]

Is it possible that space-time can be warped and curved differently from place to place in the universe? Euclidean space being flat and Minkowski is curved, So Pythagora theorem doesn't apply in curved space. But as s² = (ct)²-x² suggest that it's a universal law and all curves are the same everywhere in spacetime. Or does the curve warp? Sorry if this is a silly question but i was trying to decipher the curvage between an (all even) ball and a golf ball with indents. So given this, space-time may not be the same everywhere thus different for each observer. How does this relate to e=mc²?

[CraXshot]

Okay i'm not an expert but what I well do know in that E =mc² is Einsteins relativity theorie that states that energy(the E) have mass(the m), and with the "c" being the speed of light in a vacume( In school they say space is a vacume) so thats the only way i can relate it. I would love to know more about his theory as well if someone can perhaps post a link or just give me a basic explanation. i only made knowledge with it in order to use De Broglie's -wavelength when working with waves(Light).

Edited August 19, 2011 by CraXshot

[hawksmere]

I think that is actually a misconception. E=mc² actually means energy = mass x c (which isn't actually the speed of light but the speed of a massless partlicle) squared. We state the photons are massless but thier are studies to suggest different. Dividing E=ymc² by p =ymv leaves E/p=c²/v which for the case v=c means E=cp. Therefore, the bottom line is that energy and momentum could conceivably be nonzero even for an object with zero mass (but only if it travels at speed c. That surely gives us massless particles.

If we ever found that photons have mass (which obviously we haven't yet) we will have to c will equal 'the speed of massless particles as a universal constant'. So it is a way of measuring a constant. Not sure how it relates to ethers but that discussion always seems to run dry.

 

A good read, depending on your entry level (assuming it is non-academic) is http://www.google.co.uk/products/catalog?hl=en&q=why+does+e+mc2&gs_upl=&bav=on.2,or.r_gc.r_pw.&biw=1170&bih=724&wrapid=tljp1313766716535020&um=1&ie=UTF-8&tbm=shop&cid=15626029590403554303&sa=X&ei=Qn1OTtfyKYKAhQevvNnmBg&sqi=2&ved=0CEIQ8wIwAw

[CraXshot]

Okay thank you. No I'm still doing my last school year and I just came across it in my physics handbook but under the light module, i just know that c is the speed of light in a vacume, isnt that the same then as the speed of a massless particle?, we use it as a constant . I have not yet came across c² and just assumed that it was the same, sorry

Edited August 19, 2011 by CraXshot

[hawksmere]

No please don't be sorry because what you think is correct. I am just saying that c = photons travelling at 299mil metres per second. My point is that to date photons can only travel at this speed because they are massless so we are just giving it an association. Really what c qeuals is massless particles which just happen to be photons. I'm just being really pedantic. Your original statement is correct.

 

Do want to know more about ethers and if e=mc squared then what about the force that pulls light into a black hole?

 

Okay thank you. No I'm still doing my last school year and I just came across it in my physics handbook but under the light module, i just know that c is the speed of light in a vacume, isnt that the same then as the speed of a massless particle?, we use it as a constant . I have not yet came across c² and just assumed that it was the same, sorry

 

Also, what do you mean that speed of light in a vacume isn't the same as massless particles? Is that not suggesting that light has in fact Mass?

[CraXshot]

I dont know if you've heard of the book On The Shoulders of Giants by Stephen Hawking, but i plan on reading that in a while as well as The Universe in a Nutshell, if i dont understand the big words:) to find out more about these physics, since I love it but i'm not going to study it, youre theory makes logic sence to me but I have far too little knowledge too explain or understand it. But think about this, light can also be used in the exact same theory, for light acts like waves and have all the poperties of waves, but its also said to consist out of photons, the photon theory explains why light is also drawn towards a black holes and bending, therefore needing mass, so I do understand what you are saying, but then again , isn't time also affected by Black hole's and other Gigantic masses. Time can in that way be bent but time doesn't have mass? These theorys are all above me.

[imatfaal]

Craxshot/Hawksmere

 

c is the speed of light in a vacuum. if something changes and this has to be rethought of in the future then so be it - and the models will re-adapt, but at present c is the speed of light in the vacuum. Much as Stephen Hawking's books are great reads and he is undoubtedly a great physicist I am not sure about his pop-science books - my fave at the moment is Chad Orzel's How to teach quantum physics to your dog.

[hawksmere]

Good read i'm sure. When you talk about time i assume you're talking about spacetime. Absolute time doesn't exist, it's much more malleable and subjective. You should read some work by Faraday and Maxwell. Do you study invariance as a concept in wave studies? For e.g v=x/t, where speed is v, x is distance travelled and t is the time taken to travel the distance x. So obviously if you travel say for 60 miles and complete the journey in one hour then you are obviously travelling at 60m.p.h. But, the most interesting equations wil be those that are capable of furniching a description of nature that is agreed upon by everyone. That is, they should deal only in invariant quantities.

 

The point between any two objects in space is such an invariant quantity before Einstein's formula. So the equation v=x/t has no fundemental use as it doesn't express a relationship between invariants. It's all therefore about conjecturing: space and time can therefore be merged into a single entity that we cal' 'spacetime' and the distances in spacetime are invariant. Casuality also needs to be considered.

 

In a nutshell, time is a dimension too (i think) so you can describe it linearly. Mass, on the other hand, is a scalar quantity.

[ajb]

Is it possible that space-time can be warped and curved differently from place to place in the universe?

 

Yes, is the short answer. The curvature is a local notion and can be different at different points. (Not that we have defined curvature here)

 

The confusion maybe that the cosmological models assume that space is isotropic and homogeneous. This implies that we have a constant curvature of space. However, cosmological models take clusters of galaxies to be points, and on the scale of galactic clusters the Universe actually does look very close to being isotropic and homogeneous.

[tarekmerouani]

AT Hawksmer: it is correct that space time is in different point in space, this is called history, means that from point 1 of space time to now all sequences in the universe are registered and this is what i did explained in my blog "spaceandhistory". an other point is in the science of physics we have to introduce a new vision of how to explain physics, as I did in my blog ( Higgs boson )again by using geometric graphs anyone can understand better, so it is time to change things to be on the side of students and learners.

[TheLivingMartyr]

The actual full relativity equation is:

 

E = M²c⁴ + P²c²

 

I have lots more I want to say, but fear the consequences, and am therefore only putting what I know to be currently accepted as right '

[hawksmere]

The actual full relativity equation is:

 

E = M²c⁴ + P²c²

 

I have lots more I want to say, but fear the consequences, and am therefore only putting what I know to be currently accepted as right '

 

 

Oh please do elaborate. Is this different or an extension of Einstein's 1905 equation?

[ajb]

Oh please do elaborate. Is this different or an extension of Einstein's 1905 equation?

 

The given expression applies to any inertial frame of reference. E=mc^{2} only applies to the rest frame of the particle under question.

[redbird]

The given expression applies to any inertial frame of reference. E=mc^{2} only applies to the rest frame of the particle under question.

 

How does the second part of the equation cancel out to 0?

[ajb]

How does the second part of the equation cancel out to 0?

 

P = 0 in the rest frame of the particle under examination.

[DrRocket]

Is it possible that space-time can be warped and curved differently from place to place in the universe? Euclidean space being flat and Minkowski is curved, So Pythagora theorem doesn't apply in curved space. But as s² = (ct)²-x² suggest that it's a universal law and all curves are the same everywhere in spacetime. Or does the curve warp? Sorry if this is a silly question but i was trying to decipher the curvage between an (all even) ball and a golf ball with indents. So given this, space-time may not be the same everywhere thus different for each observer. How does this relate to e=mc²?

 

Minkowski space is also flat.

 

What need not be flat is spacetime which is a 4-dimensional Lorentzian manifold. It is the tangent space to spacetime that is Minkowski space.

 

 

s² = (ct)²-x² describes the Lorentzian metric in local coordinates, independent of any curvature (any manifold is "locally flat"). It is also locally Euclidean if one looks at local "space" so it tells you nothing about whether orb not the Pythagorean theorem holds in the large --that requires knowledge of curvature.

 

Cosmological models assume homogeneity and isotropy, which implies constant curvature. So in cosmological models space is the same everywhere. But that is true only as an approximation at the very largest scales, as ajb observed. Note that even the notion of b"space" and "time" at the global level requires homogeneity and isotropy. See this thread for more:

http://www.scienceforums.net/topic/33180-cosmo-basics/

 

This has little to do with e=mc^2 in general. The importance of the equivalence of mass and energy to this context is the effect of mass/energy on curvature since curvature of spacetime is what we call gravity. The actual large-scale curvature of space is unknown and it is, under the assumption of isotropy and homogeneity, what determines the topology of space.