# accessible in principle via algebra and geometry

June 1, 2018 10:49 AM Subscribe

minutephysics [previously: little bits of science, for SCIENCE!, dear Mr. President, OMG Science!, how to see without glasses] has a series of short videos explaining Special Relativity:

Why Is Special Relativity Hard? - We don't have to follow the same path Einstein did

Spacetime Diagrams - How motion looks from different perspectives

Lorentz Transformations - What do things look like from the moving perspective?

Relativity of Simultaneity - Events that were at different places at the same time are no longer simultaneous (at, say 1/3 the speed of light)

Length Contraction And Time Dilation - Perceiving each other's perception of time

Why Is Special Relativity Hard? - We don't have to follow the same path Einstein did

Spacetime Diagrams - How motion looks from different perspectives

Lorentz Transformations - What do things look like from the moving perspective?

Relativity of Simultaneity - Events that were at different places at the same time are no longer simultaneous (at, say 1/3 the speed of light)

Length Contraction And Time Dilation - Perceiving each other's perception of time

> then there is not any relativistic perspective in which event 2 precedes event 1

There is a way of graphing spacetime where light travels on 45 degree lines. These lines divide the world into 2 halves, a vertical light cone that gives the possible causal past and future of a point, and a horizontal "space cone" which gives the possible space-like curves through that point. So the space of light-like lines through spacetime is a boundary between the spaces of all possible time-like curves (causally-connected points), and all possible space-like curves (spatially-connected points).

What you said is equivalent to saying you can't rotate a reference frame past 45 degrees, because that would involve travelling faster than light (which travels at 45 degree angles in spacetime).

posted by I-Write-Essays at 11:23 AM on June 1, 2018 [5 favorites]

There is a way of graphing spacetime where light travels on 45 degree lines. These lines divide the world into 2 halves, a vertical light cone that gives the possible causal past and future of a point, and a horizontal "space cone" which gives the possible space-like curves through that point. So the space of light-like lines through spacetime is a boundary between the spaces of all possible time-like curves (causally-connected points), and all possible space-like curves (spatially-connected points).

What you said is equivalent to saying you can't rotate a reference frame past 45 degrees, because that would involve travelling faster than light (which travels at 45 degree angles in spacetime).

posted by I-Write-Essays at 11:23 AM on June 1, 2018 [5 favorites]

Right! That was the stuff!

and no harpy police this time

posted by thelonius at 11:26 AM on June 1, 2018

and no harpy police this time

posted by thelonius at 11:26 AM on June 1, 2018

That's why travelling faster than light is equivalent to travelling backwards in time. It tilts your reference frame angle past 45 degrees, and that lets you access points in backwards-causal order.

posted by I-Write-Essays at 11:30 AM on June 1, 2018 [2 favorites]

posted by I-Write-Essays at 11:30 AM on June 1, 2018 [2 favorites]

C = Speed of Causality

This stuff is fascinating.

BTW, PBS Spacetime on Youtube does a pretty good job unpacking a lot of the confusion around relativity in a fairly accessible but not dumbed down manner.

posted by sfts2 at 12:30 PM on June 1, 2018 [2 favorites]

This stuff is fascinating.

BTW, PBS Spacetime on Youtube does a pretty good job unpacking a lot of the confusion around relativity in a fairly accessible but not dumbed down manner.

posted by sfts2 at 12:30 PM on June 1, 2018 [2 favorites]

Yep, light is only special because it has no mass. 'c' is the speed of causality and the only things that can achieve that speed are things with no mass, like photons. At least that's my takeaway from a few relativity classes. (I think gravitons, which are the theoretical force carrier particles for gravity, would also be massless since gravity in GR also travels at c).

posted by runcibleshaw at 12:55 PM on June 1, 2018 [2 favorites]

posted by runcibleshaw at 12:55 PM on June 1, 2018 [2 favorites]

SR is very accessible via high school algebra and geometry. GR is a whole other monster and without tensors and some other pretty hairy math.

posted by tclark at 1:26 PM on June 1, 2018 [3 favorites]

posted by tclark at 1:26 PM on June 1, 2018 [3 favorites]

Episode 42: The Lorentz Transformation - The Mechanical Universe

From the 1980's, from Caltech, very overproduced, very historic. I think better explanation on the whole. Starts getting good around the 8 minute mark, but it's a lot of historical stuff intermixed with old-school graphics and explanations.

I watched this whole thing over my dads sattelite dish as a teenager, then sat in that same lecture room for an entire summer (not the same prof.) going through all 3 volumes of the green book. Good times.

posted by zengargoyle at 1:39 PM on June 1, 2018 [5 favorites]

From the 1980's, from Caltech, very overproduced, very historic. I think better explanation on the whole. Starts getting good around the 8 minute mark, but it's a lot of historical stuff intermixed with old-school graphics and explanations.

I watched this whole thing over my dads sattelite dish as a teenager, then sat in that same lecture room for an entire summer (not the same prof.) going through all 3 volumes of the green book. Good times.

posted by zengargoyle at 1:39 PM on June 1, 2018 [5 favorites]

Feynman points out that relativity of simultaneity puts some pretty strong constraints on conservation laws because it forces them to be strictly local.

If charge is absolutely conserved for example, a charged particle cannot be generated somewhere and balanced by the emergence of an oppositely charged particle somewhere else because of the relativity of simultaneity.

The uncertainty principle says that no particle can be localized at a point in space, and it seems at least somewhat paradoxical to me to say that despite this, two different particles of opposite charge (and spin) must nevertheless be at exactly the same location at the moment they come into existence when a gamma ray interacting with a nucleus creates an electron/positron pair.

Another place this rubric meets the road would seem to be at the event horizon of a black hole, where a quantum fluctuation of space itself generates a particle pair, one of which is on one side of the event horizon, and the other is on the other, so that one falls into the black hole, and the other escapes -- which is the mechanism of Hawking radiation and demonstrates the evaporation of black holes.

If such particles are charged, how is it that the creation of two oppositely charged particles simultaneously, as required by conservation of charge, yet at different locations, since they are on opposite sides of the event horizon, does not violate the relativity of simultaneity?

posted by jamjam at 2:14 PM on June 1, 2018 [2 favorites]

If charge is absolutely conserved for example, a charged particle cannot be generated somewhere and balanced by the emergence of an oppositely charged particle somewhere else because of the relativity of simultaneity.

The uncertainty principle says that no particle can be localized at a point in space, and it seems at least somewhat paradoxical to me to say that despite this, two different particles of opposite charge (and spin) must nevertheless be at exactly the same location at the moment they come into existence when a gamma ray interacting with a nucleus creates an electron/positron pair.

Another place this rubric meets the road would seem to be at the event horizon of a black hole, where a quantum fluctuation of space itself generates a particle pair, one of which is on one side of the event horizon, and the other is on the other, so that one falls into the black hole, and the other escapes -- which is the mechanism of Hawking radiation and demonstrates the evaporation of black holes.

If such particles are charged, how is it that the creation of two oppositely charged particles simultaneously, as required by conservation of charge, yet at different locations, since they are on opposite sides of the event horizon, does not violate the relativity of simultaneity?

posted by jamjam at 2:14 PM on June 1, 2018 [2 favorites]

*If such particles are charged, how is it that the creation of two oppositely charged particles simultaneously, as required by conservation of charge, yet at different locations, since they are on opposite sides of the event horizon, does not violate the relativity of simultaneity?*

Mostly because that picture of hawking radiation isn't the full picture and doesn't really accurately describe what's going on.

PBS space time has more.

posted by runcibleshaw at 2:43 PM on June 1, 2018 [3 favorites]

Black hole horizons are complicated, and our current theoretical frameworks mostly break down when trying to deal with them. It's worse than just charge conservation. It is not clear that it makes sense to talk about the inside and outside of a black hole at the same time at all. Several years ago, the AMPS paradox was proposed which shows direct contradiction between quantum mechanics and general relativity. We either have to accept that there is a firewall at the event horizon of a black hole and sacrifice the principle of equivalence, or else accept that information is lost and sacrifice quantum mechanical unitarity.

Joseph Polchinski - Black Hole Information: Spacetime versus Quantum Mechanics

Joe Polchinski - The Firewall Debate, update (Cultural Program)

Leonard Susskind - What I Learned from AMPS

I highly recommend the first lecture. RIP Joe.

posted by I-Write-Essays at 3:23 PM on June 1, 2018 [3 favorites]

Joseph Polchinski - Black Hole Information: Spacetime versus Quantum Mechanics

Joe Polchinski - The Firewall Debate, update (Cultural Program)

Leonard Susskind - What I Learned from AMPS

I highly recommend the first lecture. RIP Joe.

posted by I-Write-Essays at 3:23 PM on June 1, 2018 [3 favorites]

Neat! The mechanical spacetime diagram gizmo is very cool. I'm not sure it actually communicates more than a plot would. . . but it's a lot of fun.

As someone who sometimes attempts to teach this stuff to other people, I've used MinutePhysics' Twin Paradox video in a non-majors undergrad classroom setting (after a thorough introduction to spacetime diagrams) and everyone loved it. I suspect this set of videos is going to become a "reading assignment" next time.

posted by eotvos at 5:10 PM on June 1, 2018

As someone who sometimes attempts to teach this stuff to other people, I've used MinutePhysics' Twin Paradox video in a non-majors undergrad classroom setting (after a thorough introduction to spacetime diagrams) and everyone loved it. I suspect this set of videos is going to become a "reading assignment" next time.

posted by eotvos at 5:10 PM on June 1, 2018

Here's a fun fact: photons do not experience time at all. In their extreme reference frame they are emitted and absorbed in the same instant. (Edit to add: they do not experience distance either.)

posted by sjswitzer at 6:24 PM on June 1, 2018 [1 favorite]

posted by sjswitzer at 6:24 PM on June 1, 2018 [1 favorite]

As always, Leonard Susskind is also the best at explaining the firewall paradox. This one is a blackboard lunch lecture to non-physicists (but still technical)

posted by I-Write-Essays at 8:59 PM on June 1, 2018 [1 favorite]

posted by I-Write-Essays at 8:59 PM on June 1, 2018 [1 favorite]

*There was a young lady named Bright*

Whose speed was much faster than light.

She set out one day

In a relative way

And returned on the previous night.

Whose speed was much faster than light.

She set out one day

In a relative way

And returned on the previous night.

posted by basalganglia at 8:46 AM on June 2, 2018 [2 favorites]

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Events that were at different places at the same time are no longer simultaneousNow here's the thing that blows my mind: I have heard that, if event 1 causes event 2, then there is not any relativistic perspective in which event 2 precedes event 1. Is that right?

posted by thelonius at 11:00 AM on June 1, 2018 [1 favorite]