3 ms·

Quantum Gravity Research Could Unearth the True Nature of Time

4 points by bcaulfield 10y ago

raattgift 10y ago
This is wired reprinting an article we saw a couple of weeks ago here https://news.ycombinator.com/item?id=13095532 https://news.ycombinator.com/item?id=13095532 Last time I only said the introductory paragraph "is a grotesque of General Relativity". On second reading, I noticed it's also casting a broken version of the twin paradox wrongly as a problem in General Relativity. In the first paragraph the author casts the twin paradox as a General Relativity issue, presumably hiding behind the word "accelerate" (note the difference between quoting a word and the scare quotes the author puts around hyphenated spacetime). General Relativity is properly a theory of gravitation, and unless "at home" is close to a black hole there is no gravity to consider. Since the author doesn't include the turnaround there isn't even an apparent paradox: the traveller is simply travelling closer to "c" in a straightforward Special Relativity problem made easier with curvilinear coordinates. The author doesn't even specify that the fuel-using rocket will ever move anything but very slowly compared to the speed of light, and if that's the case, the age difference will be very close to zero for all observers. Charitably one could say that Special Relativity arises out of the structure of spacetime (it does; the Minkowski metric is induced on the tangent bundle at every point p in the manifold for the field values at p), but saying that therefore every Special Relativity problem is also a General Relativity problem is just silly or at best silly and overly pedantic. (In the normal twin paradox, A and B start at one location in flat spacetime and both using a set of coordinates with the starting point at the origin. A travels only timelike, B travels mostly relativistically. They meet again and "B" is much younger than "A". The explanation is straightforward: A's trip is extremized along the timelike axis, B's trip is not. We take the Minkowski line element ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2 and rearrange it for the proper time dT^2 = dt^2 - dx^2 - dy^2 - dz^2 and compare for each. Only dt^2 is non-zero for A; for B however at least one of dx^2, dy^2 or dz^2 is non-zero, and therefore B's dT^2 is smaller than A's. We can do the same for practically any set of coordinates -- e.g. in spherical coordinates the line element is ds^2 = -c^2 dt^2 + dr^2 + r^2 d\theta^2 + r^2 sin^2(\theta) d\phi^2, so dT^2 = dt^2 - dr^2 - r^2 d\theta^2 - r^2 sin^2(\theta) d\phi^2, and again A's dT^2 is less than B's, because ds^2 and dT^2 have the same value under the new coordinate system. If B accelerates then we are likely to want use a system of coordinates which is useful for accelerated observers in flat spacetime -- typically curvilinear ones -- but we still end up comparing values of dT^2. And fundamentally the explanation for this is in the structure of flat spacetime: its local symmetries, notably the Poincaré isometry group at each point, generate the Minkowski metric.)

4 points by bcaulfield 10y ago

This is wired reprinting an article we saw a couple of weeks ago here https://news.ycombinator.com/item?id=13095532 https://news.ycombinator.com/item?id=13095532 Last time I only said the introductory paragraph "is a grotesque of General Relativity". On second reading, I noticed it's also casting a broken version of the twin paradox wrongly as a problem in General Relativity. In the first paragraph the author casts the twin paradox as a General Relativity issue, presumably hiding behind the word "accelerate" (note the difference between quoting a word and the scare quotes the author puts around hyphenated spacetime). General Relativity is properly a theory of gravitation, and unless "at home" is close to a black hole there is no gravity to consider. Since the author doesn't include the turnaround there isn't even an apparent paradox: the traveller is simply travelling closer to "c" in a straightforward Special Relativity problem made easier with curvilinear coordinates. The author doesn't even specify that the fuel-using rocket will ever move anything but very slowly compared to the speed of light, and if that's the case, the age difference will be very close to zero for all observers. Charitably one could say that Special Relativity arises out of the structure of spacetime (it does; the Minkowski metric is induced on the tangent bundle at every point p in the manifold for the field values at p), but saying that therefore every Special Relativity problem is also a General Relativity problem is just silly or at best silly and overly pedantic. (In the normal twin paradox, A and B start at one location in flat spacetime and both using a set of coordinates with the starting point at the origin. A travels only timelike, B travels mostly relativistically. They meet again and "B" is much younger than "A". The explanation is straightforward: A's trip is extremized along the timelike axis, B's trip is not. We take the Minkowski line element ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2 and rearrange it for the proper time dT^2 = dt^2 - dx^2 - dy^2 - dz^2 and compare for each. Only dt^2 is non-zero for A; for B however at least one of dx^2, dy^2 or dz^2 is non-zero, and therefore B's dT^2 is smaller than A's. We can do the same for practically any set of coordinates -- e.g. in spherical coordinates the line element is ds^2 = -c^2 dt^2 + dr^2 + r^2 d\theta^2 + r^2 sin^2(\theta) d\phi^2, so dT^2 = dt^2 - dr^2 - r^2 d\theta^2 - r^2 sin^2(\theta) d\phi^2, and again A's dT^2 is less than B's, because ds^2 and dT^2 have the same value under the new coordinate system. If B accelerates then we are likely to want use a system of coordinates which is useful for accelerated observers in flat spacetime -- typically curvilinear ones -- but we still end up comparing values of dT^2. And fundamentally the explanation for this is in the structure of flat spacetime: its local symmetries, notably the Poincaré isometry group at each point, generate the Minkowski metric.)