My lecturer says "Special relativity is absolutely wrong"

[Warp]

The simple version of the situation is: Nothing can travel faster than c, but under certain circumstances the distance between two points can increase faster than c. (At first glance they might sound like the same thing, but they are not.)

 

[PAllen]

The simple version of the situation is: Nothing can travel faster than c, but under certain circumstances the distance between two points can increase faster than c. (At first glance they might sound like the same thing, but they are not.)

Correct observation. Note that this is as true in SR as in GR. Consider the simple case of an inertial frame in SR, with object A moving to the left at .9999...c and B moving to the right at .999...c. Then the distance between them grows by 1.9999...c [despite their relative velocity being <c]. Using a flat space analog of cosmological coordinates, you can get a separation speed between inertially moving bodies of any multiple of c. Note, this distance is integrated proper distance so it is not a matter of coordinate units. It is instead, a matter of how flat spacetime is foliated by the coordinates. In particular, each spatial slice being hyperbolic in geometry is what allows this result.

 

[Warp]

Note that this is as true in SR as in GR.

I don't see how. SR states that nothing can travel faster than c, no matter what. It doesn't matter what the relative velocities are between the observer and the object, when the observer measures the velocity of the object, it will always be under c.

The reason why under certain circumstances the distance between two points can genuinely grow faster than c is because of non-linear spacetime geometry, a concept that only GR introduced.

Consider the simple case of an inertial frame in SR, with object A moving to the left at .9999...c and B moving to the right at .999...c. Then the distance between them grows by 1.9999...c [despite their relative velocity being <c].

I don't think that's how SR works at all. You can't just sum velocities like that.

 

[PAllen]

I don't see how. SR states that nothing can travel faster than c, no matter what. It doesn't matter what the relative velocities are between the observer and the object, when the observer measures the velocity of the object, it will always be under c.

Wrong. While the velocity of A relative to B, measured by B, or vice versa, is < c, the growth rate of separation between A and B can approach arbitrarily close to 2c in a given inertial frame. This is exactly why comparing separation rate to relative velocity is a category error, like comparing temperature to energy.

I

The reason why under certain circumstances the distance between two points can genuinely grow faster than c is because of non-linear spacetime geometry, a concept that only GR introduced.

This is false. I made my observation because a surprising number of cosmology presentations make this error. If you take the limit of FLRW solutions to a massless universe, you end up with flat spacetime (i.e. pure SR) in Milne coordinates. These foliate the flat spacetime with hyperbolic spatial slices. The growth of proper distance (along these hyperbolic spatial slices) between inertial world lines that are part of the homogeneous congruence of the solution can by any multiple of c whatsoever (if they are far enough apart). Yet, this is pure SR minkowski spacetime.

I

I don't think that's how SR works at all. You can't just sum velocities like that.

The velocity addition formula applies to relative velocities. Separation rate (= recession rate) is a completely different category, that is just as unbounded in SR as it is in GR. I highlight this because of the large number of false statements in this regard by cosmologists making a category error. Note that Sean Carroll who has written a great GR text as well as being a notable cosmologist, has written on this point, and does not make this mistake.

 

[Warp]

This is false.

So what you are effectively saying is that the size of the universe is exactly the size of the observable universe, because the metric expansion of the universe cannot make distances between galaxies grow faster than c. After all, the claim that changes in the geometry of spacetime can cause distances to grow faster than c is "false".

Also ergospheres around rotating black holes do not exist, because the concept is "false".

You learn something new every day.

 

[PAllen]

So what you are effectively saying is that the size of the universe is exactly the size of the observable universe, because the metric expansion of the universe cannot make distances between galaxies grow faster than c. After all, the claim that changes in the geometry of spacetime can cause distances to grow faster than c is "false".

Also ergospheres around rotating black holes do not exist, because the concept is "false".

You learn something new every day.

No, you completely misunderstand (charitably; uncharitably, you deliberately and sarcastically distort) what I wrote. I wrote that distance between between inertial bodies can grow faster than c in both flat spacetime and curved spacetime, depending on the foliation. You state this somehow implies that distance cannot grow faster than c. This is the opposite of my claim - that distance can grow faster than c in either SR or GR.

 

[Warp]

No, you completely misunderstand (charitably; uncharitably, you deliberately distort) what I wrote. I wrote that distance between between inertial bodies can grow faster than c in both flat spacetime and curved spacetime, depending on the foliation. You state this somehow implies that distance cannot grow faster than c. This is the opposite of my claim - that distance can grow faster than c in either SR or GR.

I think there is a fundamental misunderstanding in all of this.

If I'm an observer and am measuring a (massive) object receding from me, according to SR I will never, ever measure said object to be receding from me faster than c, or even at c. It may approach c, and thus may red-shift to almost invisibility, but it will never reach c, and thus never become completely invisible.

However, according to GR the receding object can recede from me faster than c. It thus becomes completely unobservable from my perspective, effectively being beyond an observability horizon. And there is effectively no limit to how much faster than c it can recede. SR does not have this concept because it considers space to be linear and static.

 

[Ibix]

@Warp - you are depending on a particular simultaneity criterion (a flat foliation of flat spacetime) to make your statements. @PAllen is using a different, but still perfectly reasonable, simultaneity criterion (a curved foliation of flat spacetime). He's applying GR tools to SR, but he's still talking SR.

If I understand right, you can visualise spacetime as a block. You are slicing it into flat planes and calling each plane "the universe at time t". He's slicing the block into a stack of bowls and calling each bowl "the universe at time t". Spacetime is still the same 3d block, whichever way you slice it, but your definition of space is different so your definition of speed through space is different.

 

[martinbn]

Warp, you are confusing yourself. Shine light to the right and to the left. Each beam travels at speed c. What is the velocity (rate of change) of the separation of the fronts of the two beams? Let's calculate. After 1s, the right beam will be 300000km to your right, the left that much to your left. So the distance between the two has changed from 0 to 600000 in 1s, thus the speed is 2c.

 

[Battlemage!]

I don't go along with this business of 'ordinary language' being sterile whereas math has some 'rich underlying meaning'.

In reality, what that means is that physicists don't have a sufficiently eloquent grasp of language to enable them to translate their mathematical symbols into the appropriate and corresponding terminology. Which is not surprising as it's difficult to wield expertise in two disparate subjects.

At the end of the day every mathematical concept can be expressed linguistically, but not vice versa.

Even if you expressed an abstract mathematical concept linguistically, it could still be far beyond the ability for someone not mathematically inclined to grasp. They could recognize where the nouns and verbs are, but the idea being communicated in the words could still be inaccessible to them.

In fact, writing abstract mathematical ideas in words rather than math symbols would very likely make the concepts harder to understand, not easier.

Regardless, words won't help someone understand a concept they are unprepared to understand. This can be readily seen in the definition of a limit. When you PRECISELY describe it in words, using the epsilon-delta definition, the idea can be very difficult to grasp for someone not familiar with that sort of thing. But simply saying "some value this function approaches" is extremely imprecise. And then when you start making more abstract definitions that depend on previous ones things would get very confusing if written in everyday words. Regardless of the way they are written, if you don't have a good understanding of mathematics you aren't likely to grasp what you read.

 

[RockyMarciano]

Science needs philosophers of science like birds need ornithologists.

Funnily enough, you might not not fully acknowledge that your meta-comment is pure philosophy of science.
Whether it s good or bad philosophy is a judgement that can be left to the reader.

 

[andrew s 1905]

Even if you expressed an abstract mathematical concept linguistically, it could still be far beyond the ability for someone not mathematically inclined to grasp. They could recognize where the nouns and verbs are, but the idea being communicated in the words could still be inaccessible to them.

Equally one could understand the mathematics perfectly and have no clue as to the physical implications or completely misunderstand them. I think we should accept there is a continuum from a full understanding of a physical theory through a more or less hazy understanding to complete ignorance. This will span physicists and non physicists alike.

Regards Andrew

 

[PAllen]

I think there is a fundamental misunderstanding in all of this.

If I'm an observer and am measuring a (massive) object receding from me, according to SR I will never, ever measure said object to be receding from me faster than c, or even at c. It may approach c, and thus may red-shift to almost invisibility, but it will never reach c, and thus never become completely invisible.

However, according to GR the receding object can recede from me faster than c. It thus becomes completely unobservable from my perspective, effectively being beyond an observability horizon. And there is effectively no limit to how much faster than c it can recede. SR does not have this concept because it considers space to be linear and static.

Let me try again to get across what your category error is.

In SR, if I measure the speed of an object relative to me, it will always be less than c. However, if I measure the rate of growth of proper distance between between two objects, the result can be up to 2c in an inertial frame, and any value in a non-inertial coordinates (even though I ams still talking about growth of proper distance with respect to proper time of a fiducial observer). The flat space analog of cosmological coordinates is a non-inertial frame (known as Milne coordinates). Note that these coordinates have a cosmological horizon (and do not completely cover all of Minkowsi space). Also, note that as simple as case as a uniformly accelerating observer in SR sees a Rindler horizon form behind them, and objects beyond it become causally disconnected from them. Infinite redshift occurs as an object approaches said horizon, and there is no signal, let alone redshift possible for an object beyond the Rindler horizon.

In going to GR, we have to look more at what relative velocity means. In SR you can define it either as speed in a global inertial frame in which one of the objects is at rest. Or you can define it in terms of 4-vector comparison (dot product of two 4-velocities gives gamma of their relative speed), relying on the fact that parallel transport in SR is path independent, thus distant vectors can be unambiguously compared. Note that it is only relative velocity in one of these senses that is limited to c in SR, as noted above. Unfortunately, in GR, neither of these definitions work at all. Globally inertial frames do not exist; parallel transport is path dependent so there is no such thing as comparison of distant vectors. As a result, relative velocity does not exist in GR except locally (where you can use a local inertial frame; equivalently, vectors at the same event can be compared unambiguously because parallel transport is not necessary). Of course, this local relative velocity in GR is always < c.

Globally, in GR, all you have are analogs of the coordinate dependent quantities described above, that are not limited to c in SR. These things (including recession rate) do not correspond to SR relative velocity at all. There is a limited statement you can make globally in GR that is in the same category as SR relative velocity. That is: while the relative speed of distant objects is inherently ambiguous because of path dependence of parallel transport, no matter what path you use for parallel transport, the result of parallel transport followed by vector comparison is always < c, with no exceptions. Thus there is no way to choose a specific value, but the range of admissable values are all < c.

 

[gjonesy]

Even if you expressed an abstract mathematical concept linguistically, it could still be far beyond the ability for someone not mathematically inclined to grasp.

I totally agree in some cases that would be absolutely 110% true, in others there is a gray area, some of the common language used to describe SR and GR have slightly different meanings then they ordinarily would have. In certain cases where someone is making an genuine effort to learn (some of the) concepts and you have a patient teacher who can get those meaning across linguistically by making clear that "common language" isn't adequate and by saying "this" I actually mean "that" you can actually learn (some of the) the concept. I have learned certain things about physics and I "know" it I just can not express it to others the same way because I lack the expertise to translate what I know.. BUT the ones who have taken the time and went over things with me and who have been patient do have this gift of translating (some of the) material. Not all of it can be expressed this way and I will probably never have a full understanding of it and I fully accept it. But the parts that I have been able to grasp are like pearls of wisdom. And that is what's so great about this forum, you have people here who can do that.

 

[Dale]

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