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4

The thrower's height doesn't change i.e. it is the same in both the reference frames of the thrower and the bug. That's because distances normal to the direction of motion are not changed by Lorentz transformations. In the bug's frame the thickness of the thrower decreases, so the thrower is flattened in the direction of motion, but the height is unchanged. ...


0

OK, just one more try to end this stupid question. There IS a way to formulate physics using light rays as your basis: a double null coordinate system${}^{1}$. If you have a ray moving in the $+x$ direction, define the two coordinates $$2\xi = t + x\;\;\quad\quad\quad2\eta = t - x$$ Then, the metric becomes $$ds^{2} = -4d\xi \,d\eta + dy^{2} + dz^{2}$$ ...


1

The common definition of "time" is a type of measurement, like size. No. The common definition of "time", certainly in the context of physics, is as one indication of one participant, or also as the ordered set of all indications of one participant. As Einstein put it: "[... that instead] of "time" we substitute "the position of the little hand of my ...


0

In terms of physics time is a coordinate and defines a coordinate system . In the newtonian world we live our lives in, time is fixed by clocks and space by rulers. Slowing or acceleration of time is a personal perception, old people feel time passes very fast, in crisis situations it passes very slowly in the observer's perceptions. If one goes into ...


0

Instead of using existing spacecraft, let's use a photon rocket powered by the gamma rays emitted by matter anti-matter annihilations in its reacor. Where does the anti-mater come from? We will produce it using solar energy. We'll use giant solar panels that generate a huge voltage in vacuum which leads to Swinger pair production. Moving away from the Earth ...


0

From ScienceMuseum: Apollo 10 holds the record as the fastest manned vehicle, reaching speeds of almost 40,000 km per hour (11.08 km/s or 24,791 mph to be exact) during its return to Earth on 26th May 1969. Using the formula (as above). After traveling for 40 years, you would be a little over 0.86 seconds younger. Added: I did some calculating and ...


2

Almost none. Let's be much more generous than your idea of human-carrying craft. Let's just use the fastest probe. The Helios II craft, after nearing the sun, reached a heliocentric speed somewhere near 70 km/s. Obviously, its speed was more due to the gravitational influence of the sun than its engines. $$t = \frac{t_o}{\sqrt{1 - \frac{v^2}{c^2}}} $$ ...


2

So let's just say that the spacecraft can accelerate until it's moving away from the Earth at the speed of the fastest currently-existing spacecraft First, note that the fastest speed, relative to Earth, that a spacecraft has obtained is an exceedingly small fraction of the $c$ and, thus, one should not expect significant time dilation. For ...


0

Your notion seems to be based on the thinking that light is a bunch of photons, and a photon is some kind of weird particle that travels at the speed of light, like some tiny spaceship. Then you ask, how can this tiny spaceship violate physical laws? What makes it so special? But a photon isn't a particle in any classical sense. It's not like a tiny ...


0

Special relativity states: ... I'll select and discuss the given statements in some particular order (which may be called "in order of simplicity of discussion") ... [...] The observer is (anything [...]) Right. Synonymous to "observer" or "anything", in the context of the theory of relativity, there are also the descriptions "material point" or ...


3

I will expand my comment above into an answer, but I will not comment further on it to avoid the usual very long discussions of your posts. In my opinion, you are trying to argue on a logical level, but it is not clear if you have enough knowledge of logical theories to do so on a mathematical/physical level. Without entering too much into details, a ...


10

To make progress we need to be clear what we mean by the laws of physics and observer. A law of physics is just some set of equations that we use to predict what happens. So if for example we're trying to describe how charges interact with light our set of equations, i.e. our law of physics, would be Maxwell's equations. But to write down Maxwell's ...


0

Things are much simpler here if one thinks in terms of spacetime events and their coordinates in the relatively moving reference frames. As best as I can tell, there are three events of interest: Event A: two photons are emitted from station A Event B: one of the photons is received at station B Event C: the other photon is received at station C ...


-1

Your calculation refers to time intervals between two events inside the ship, as seen from a different reference frame (Earth?), and in Special Relativity this is equivalent to what would be seen from the ship if in the other reference frame the same experiment was being performed. However this is not the correct way to solving the paradox, this paradox ...


1

I do not find easy to understand your calculations, but can give you an explanation which is not based on specific distances. It is easy to see why the observer inside the ship will perceive the events as simultaneous and the one outside the ship will not. First, notice that for every observer the speed of light is the same, c. So the observer on the ships ...


2

Events which lie within each other's light cones are called "timelike separated." All observers agree on the ordering of these events. Events which lie on each other's light cones are separated by "lightlike" or "null" interval. All observers also agree about the time ordering of these events. Events which lie outside of each other's light cones are called ...


0

"I've been pondering the implications of time dilation. " - thar be dragons! :) The answer to the question is no, of course. Per the previous answers you have to consider frame of reference which in space time is arbitrary. Time dilation is how you resolve the problem of two objects traveling directly towards each other at > .5C per a 'stationary' third ...


2

that to an external observer it would appear to be moving very much slower? I don't understand the reasoning here. When you write assume that if a craft was travelling at a speed very close to the speed of light I take that to mean that the craft is travelling very close to the speed of light according to an external observer. Keep in mind ...


3

No. Time-dilation is the slowing of time as experienced by the fast moving craft, not the 'stationary' observer. Remember that light moves at c, and we see it move at c, not some slower or stationary speed. As the craft approaches c, it appears to accelerate increasingly slowly; from 0.99999c to 0.999999c is only a difference of 2.7 km/s, but it is still ...


0

If I travel at relativistic speed ... let's say at constant speed $\beta ~ c$ ... from planet A to planet B which are at rest relative to one another then (1) A and B succeed in determining which indication of A had been simultaneous to which indication of B (and vice versa); and (2) A's duration from indicating your departure, until the (A's) ...


0

You have got a synchronization problem because you are describing 2 events (departure planet $A$ and arrival planet $B$), but there are 4 events in spacetime to be taken into account (state of planet $B$ at the departure and state of planet $A$ of the arrival are missing). The contradiction is relatively simple to track, only applying the time dilation ...


4

so when I arrive at B why would I be younger? I believe I addressed this in another question of yours. Once again, assume that when you pass planet A, your clock and planet A's clock both read $t = t_A =0$. Now, according to the inhabitants of planet A, planet B's clock is synchronized with their clock. However, in your inertial frame of reference, ...


0

While travelling in an inertial reference frame, you perceive the time of objects moving relative to you to go slower than your time. For such situations, you may apply the naive notion of time dilation. As soon as you accelerate anywhere, you should forget about time dilation as a way to gain what you will read on any clock. Time dilation is not the only ...


3

You shouldn't use the "subjective/objective" distinction for a place where "relative/absolute" is much more appropriate, because they mean different things. For something to be subjective, it must be dependent on the knowledge or state of mind of an observer. As an example, suppose we define "depth" as "length along the direction an observer is facing". ...


2

It means that time is no longer an absolute concept, yes. The time a specific observer experiences in a specific frame of reference, i.e. his proper time depends on the path (worldline) he takes through spacetime. In other words, it depends on his state of motion, the way he accelerates. This is the reason for the famous twin paradoxon: the resolution is ...


0

The proper time between two space-time points is very, very like the ordinary distance between two points in ordinary space. In fact, in the case that the two points are at the same time in a given frame the proper time between them is just (minus) the distance between them divided by c, the speed of light. It does not require a clock to be real, any more ...


0

As stated by Moonraker your point C is the same as saying there is no space at all thereby any definition of 2 points makes no sense at all. Now to the question "what is proper time?" "It is the time which is measured in the rest frame of an observer passing through two events in space-time" This will depend on the kind of movement the observer ...


2

Ok, before we fill up the comment section with this, I will write this as an answer: Proper time $\tau$ along a path $\gamma$ is $$ \tau := \int_\gamma \sqrt{\mathrm{d}x^\mu\mathrm{d}x_\mu}$$ and a clock moving along $\gamma$ will have $\tau$ as its elapsed time at the end of the path. Yet, the definition of proper time $\tau$ involves such clocks not ...


1

If the two laser beams are emitted at the same moment in one frame, they will not be emitted at the same moment in another frame moving relative to the original frame. This is relativity of simultaneity. Since the light beams start at different times, it's not a problem for them to travel a different distances.


5

Yes, that's ok! You've stumbled upon one of the basic strange phenomena of relativity.



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