40 votes

Why would black hole rip me apart?

You don't need GR to see this effect. It's due to tidal forces. Suppose you are 2 meters tall. Then the force of the Earth on your feet is $GMm/r^2$, and the force on your head is $GMm/(r+2)^2$. The ...
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30 votes
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Why would black hole rip me apart?

The problem is that when you are falling, all of you can't be in the same inertial frame. That is, whilst your centre of mass might be inertial, parts of your body will be feeling accelerating forces ...
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  • 110k
9 votes
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How could any frame of reference be inertial?

In newtonian mechanics, inertial frames are an equivalence class. They can be defined as frames where Newton's laws are valid. If you can find one inertial frame, then you automatically get an ...
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  • 588
4 votes
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Dependence (or lack thereof) of forces on frames of reference

When you say "blocks A and B move with a relative acceleration of -3 m/s2" you are considering the motion of one block in the reference frame attached to the other block (block C). But the ...
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  • 6,270
4 votes
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Riemann curvature tensor in an inertial frame

The fact that a function's first derivative vanishes at a point does not mean that its second derivative vanishes at that point. Note that for $f(x)=x^2$, $f'(0)=0$ but $f''(0)=2$.
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3 votes

Are Newton's laws just definitions?

From a mathematical point of view, they are definitions: they relate mathematical abstractions. But from a physical point of view, they are not definitions: they capture real behavior of real physical ...
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  • 3,204
3 votes
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Invariance of spacetime interval by Schutz

The claim is that if the relationship between coordinates in the two inertial frames is linear and if $\Delta S^2 = 0$ necessarily implies that $\Delta S'^2 = 0$, then in general we must have that $\...
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  • 50.7k
3 votes

Simple resolution to the twin paradox?

I'm sorry, Jacques, but as you suspected your explanation is incorrect. The twin paradox seems paradoxical because time dilation is entirely symmetrical, so both Bob and Alice might be expected to be ...
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  • 18.2k
3 votes
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Is angular momentum conservation Galilean invariant?

The answer is no. To begin with, a Galilean transformation in three dimensional Euclidean space(time) consists of space-time translation: $(t,\vec{x})\rightarrow(t+s,\vec{x}+\vec{a})$ spatial ...
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3 votes

Argument of a scalar function to be invariant under Lorentz transformations

A scalar Lorentz invariant function satisfies $$ f(k) = f(\Lambda k). $$ for all $\Lambda$ satisfying $\Lambda^T \eta \Lambda = \eta$. Let us look at the infinitesimal version of this equation. ...
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  • 20.4k
2 votes

Problem with Inertial reference frames Rider on a merry-go-round

If the round-about is inside a train and protected from the breeze. Then the experience of the the rider will be independent of the constant speed of the train. (Consider your experience inside a ...
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  • 11.4k
2 votes
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Error in Derivation of Time Dilation Formula

The time dilation formula is a special case that applies only to the interval between two events that are in the same location in one frame and in two different locations in another. The example you ...
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  • 18.2k
2 votes
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How is a locally inertial frame possible in Principle of Equivalence of General Relativity?

In the context of General Relativity, the "lab frame" is not inertial, because it is not freely falling. This is the point of Einstein's "elevator" thought experiments: a freely ...
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2 votes

Explanation for invariance of $c$ / Lorentz transformations?

The modern view of special relativity is as a geometric theory, with time dilation and similar effects explained as a consequence of different observers having different directions in 4D spacetime as ...
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2 votes
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Time derivative relation between two rotating frames

$$ (1) \Big(\frac{d}{dt}\Big)_{rot_1} r(t) = \Big(\frac{d}{dt}\Big)_{in}r(t) - \Omega_1(t) \times r(t) $$ where $rot_1$ denotes a coordinate system rotating at $\Omega_1(t)$ relative to the fixed ...
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  • 5,825
2 votes
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Show Energy-momentum operator transforms as a tensor under Lorentz transformations

In regards to your first question, that is, in fact, a definition. To appreciate it, let's recall what a representation is. Let $G$ be some group. A representation of $G$ is a pair $(V,D)$ where $V$ ...
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  • 29.2k
2 votes

Relativity of simultaneity in special relativity

In the example of the Einstein train, if both the bystander and the train passengers know of the train movement, there is no reality relativity, there is an absolute state of the universe, right? Not ...
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  • 64.3k
2 votes
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Are curvilinear coordinates inertial?

Indeed, it is valid to consider that polar coordinates are non-inertial. You should be aware that the term “reference frame” does not have one unique meaning. Different authors may use it to mean ...
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2 votes
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Is gravity a direct result of Lorentz Contraction?

No. Special relativity on its own doesn't imply general relativity. It's not enough to have some invariance principles; you need to "turn on" mass-energy gravitating by specifying how they ...
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  • 21.7k
2 votes

Invariance of spacetime interval by Schutz

I would suggest you read Landau & Lifshitz argument for invariance of $ds^2$, particularly the Wikipedia link because it states clearly the theorem which is being proved, and it fills in a few ...
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  • 2,269
2 votes

Why would black hole rip me apart?

There are nice answers by @fraxinus and @profrob, I would like to add a little side note about the balance between the forces. It arises because the gravitational field exerted on one body by another ...
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2 votes

What does size of an inertial frame mean?

I've never seen it phrased like that, but I understand it as the following. Strictly speaking, the frame is defined locally, on a point. So the further you move from that point, the less inertial the ...
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2 votes
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What does size of an inertial frame mean?

The Equivalence Principle (EP) is valid locally: if you perform a local experiment in an inertial frame of reference, you can't say if you're freefalling or not falling, you can't say if you're ...
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2 votes

Why does four-momentum have the same transformation matrix as spacetime coordinates?

four-momentum is literally the first (proper) time derivative of position, multiplied by mass, so it is a vector with the same transformation rule.
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1 vote

How to represent a pair of inertial frames in relativity?

In Special Relativity we couldn't say in general that the axes of two inertial frames $\:\rm S\:$ and $\:\rm S'\:$ in relative translational motion (boost) are parallel, see Figure-02, except of ...
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1 vote

Simple resolution to the twin paradox?

The calculation you performed clearly shows that distance depends on the observer. This does not resolve the twin paradox since if Alice does the math instead of Bob's perspective then you would get ...
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  • 788
1 vote
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Are Newton's laws just definitions?

Your statements starting with "in an inertial reference frame" are indeed trivially true, because of the definition of the inertial frame: inertial frame is a frame where the first and the ...
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1 vote

Are Newton's laws just definitions?

Newton's first law is usually taken as the definition of an inertial frame. Hence it is not a special case of the second law, and resolves your concern of the second bullet point regarding the second ...
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1 vote

Is angular momentum conservation Galilean invariant?

But this doesn't make sense to me because the rotational invariance of a system doesn't seem to change when I change to a new inertial reference frame. It can change. Torque depends on origin. As an ...
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1 vote
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FTL travel without time travel (again)

It seems to me we can change the thought experiment so that it is real FTL travel without time travel by slowing the FTL speed to less fast but still FTL speed I think this answer does a good job of ...
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