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3

Mathematically, that's due to superposition. Both masses produce some gravitational field, which add together to give the "net field". (The same goes for electromagnetism, where one may add electric/magnetic field strengths,electric potentials etcetera for every point in space.) Ever so slightly changing the field strength at the well. As gravity gets weaker ...


2

If two events both have a spacetime interval of zero, can they both be said to be happening “now”? There is an interval associated with any two events but there is not an interval associated with an event. From the Wikipedia article "Spacetime": In spacetime, the separation between two events is measured by the invariant interval between the ...


1

I'm not sure this is a complete answer to your question, but thinking about special relativity that way will get you into trouble. Essentially, that way of interpreting special relativity attributes all of its weirdness to signal delay. Here's how I think you're interpreting the barn door experiment: The ladder is put stationary in the barn and is found to ...


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 $$ds^{2} = -4d\xi \,d\eta + dy^{2} + dz^{2}$$ ...


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 ...


2

The planck length is not necessarily an absolute limit to how small thing can be sub divided. The planck length is theoretical and it is empirically defined by dimensional analysis. At this length scale our knowledge of physics makes no sense. The planck length $\ell_P$ is defined as: $\ell_\text{P} =\sqrt\frac{\hbar G}{c^3} \approx 1.616\;199 (97) \times ...


1

Space-time is thought to curve and ripple. Space-time, i.e. the set of all events under consideration (specificly: coincidence events), together with all relations between these events (primarily: by listing who, among all principal identifiable participants, took part any one coincident event), is thought to be not necessarily homogenous and/or ...


1

This is an open problem, the problem of Time in General Relativity and Quantum Gravity (e.g here and here). The solution would require a synthesis of General Relativiy, Quantum Field Theory and especially Thermodynamics (the 2nd Law). Many people, due to the treatment of time parameter in general relativity, take a stance that time is an illusion (sth this ...


3

I've said it before and I will say it again: There are no frames travelling at the speed of light As David Z says in the very link you give, it is meaningless to ask what you would perceive travelling at the speed of light. You cannot. And even though there are particles that can, there are no frames associated with them. Have a look at the Lorentz boost. ...


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 ...


3

You're asking two separate questions. To take your second question first, the existance of seven extra spacelike dimensions is a requirement for the consistency of string theory and we have no experimental evidence that extra dimensions exist or that string theory is a good description of reality. So it's impossible to make any definitive comment about why ...


0

To address the issue of "...then how exactly does this illusory sensation of 'now' work", let's consider the mathematical multiverse mentioned in Julian Fernandez' answer above. If you take this seriously, then you should consider yourself to be a mathematical algorithm. A mathematical algorithm can be defined by consdering how it acts on certain states, but ...


3

Why time is considered to be a dimension? Because, to the extent of the empirical evidence, relatively moving inertial observers are related by the Lorentz transformation. But, the Lorentz transformation mixes time and space coordinates in a particular way. If time were not a dimension, if time were just a universal parameter, this mixing would not be ...


4

I think you should understand the passage a bit more abstractly: Take the space $\mathbb{R}$. It's obviously one-dimensional. Now, consider the space $\mathbb{R}\times\mathbb{R} = \mathbb{R}^2$, the vector space over $\mathbb{R}$ with two dimensions. You have thus created a two-dimensional object from a one-dimensional one. Let us now construct the book: ...


0

In note [5] of your paper, check the recent paper The physics of 'now', James B. Hartle. Hartle builds models of simple information gathering and utilizing systems and explains how past, future and now may be concepts describing IGUSes process information. It is interesting to point out different IGUSes can have drastically different and bizzar notions of ...


0

The red (blue) shift of light from gravitational potential is obvious because it is proven by experiments. on the over side the constance of c is part of the concept of Einstein's special theory of relativity. It's the basis for all over considerations. But the gravitational potential doesn't play any role at this moment. Later in his general theory of ...


1

Even if there is no agreement in the physics community about what is special about "NOW", I believe that most physicists that believe in a block universe would agree with your statement that there are an infinite number of me's at every point in time, all experiencing their own now. Not only that, there is an infinite number of mathematical universes (see ...


1

Then A will observe that B's time is elapsing more slowly than its own. It will also notice that B is shorter in the direction of travel than A is. But, it is also true that B will observe that A's time is elapsing more slowly than its own and B will also notice that A is shorter in the direction of travel than B is. This is because motion is ...


1

You seem to be interested in the concept of dualities. Dualities are incredibly informative in Physics in that every time we've come across one, it's led to unification of the two dual entities. You've already stated the most common one of spacetime. This was of course unified by relativity. You mentioned the Mass-Energy duality. This arises right from ...


2

The idea is that the object generating the "pit" in the front is in the center of the flat region in the middle. What happens is that the object in the middle begins to "fall" into the "pit" in front of it, due to gravitational attraction. The "pit", however, moves forward because it is a fixed distance away from the object in the middle. Basically, as ...


1

No, and the reason is quite simple. The proper time of a photon is zero (according to the principles of special relativity). That means that there is no time difference between the place of emission and absorption. By this, any hypothetical observation of a photon would be reduced to a time period of zero, and it would not be able to distinguish/ to ...


4

Imaginary time has no physical meaning. It is an assumption physicists make, namely, that the math will endure the analytic continuation of the time variable onto the complex plane, which makes some calculations easier, but it is not absolutely necessary (e.g. you can do instantons without imaginary time).


6

In special relativity, the metric on spacetime is $$\mathrm{d}s^2 = \mathrm{d}x^2 + \mathrm{d}y^2 + \mathrm{d}z^2 - \mathrm{d}t^2$$ (or with inverted signs). If you now formally transform $t \mapsto \mathrm{i}t$, this becomes the familiar Euclidean metric on $\mathbb{R}^4$ $$\mathrm{d}s^2 = \mathrm{d}x^2 + \mathrm{d}y^2 + \mathrm{d}z^2 + \mathrm{d}t^2$$ ...


0

First, one must be careful to distinguish observation in Special Relativity from what I think it is you have in mind. It's true that the clock will be observed (in the SR sense of the word) to run slow. However, if what you're interested in is your proper time between reception of the light pulses, keep in mind that this is a different notion than observe ...


1

Now take a third clock, clock C, which is also synced with A and B and have it travel the distance between A and B at .866c That's impossible. Let clock C, traveling at $0.866c$, pass by clock A just when both clocks read $t_C = t_A = 0$. Now, according to clock A, clock B also reads $t_B = 0$ at this instant. But, according to clock C, clock B ...


1

In special relativity the rule of thumb is Moving Clocks run slowly. So in your inertial reference frame. The clock is moving towards you at 0.866c and thus is running slower than a clock you keep in your frame of reference. This means the clock will pulse out the light less often. With the light coming towards you at 1.00c and you moving towards it ...


2

You are still trying to use intuition about space-time that is simply wrong. Experimentally wrong. The world doesn't work the way you (and I) think it does. Spatially separated clocks can not be synchronized in all frames. No, really. They can't. If you synchronize clocks A & B in their common rest frame (which can be done) then they are unavoidable ...


0

After reading this and your other question I'm going to recommend you try to find a copy of this book, Modern Physics for Scientists and Engineers by John R. Taylor. It has great explanations on special relativity especially these weird ones. The geometry of your problem is critical. When you say C trave;s the distance between A & B do you mean it runs ...


0

I said this already on your last post, but you should really lay time dilation to rest and consider that the time a clock travelling along a path $\gamma$ reads will be the proper time $$\tau = \int_\gamma \sqrt{\mathrm{d}x^\mu\mathrm{d}x_\mu}$$ (it even explains the twin "paradox" on the page!). As proper time is an invariant, it suffices to calculate it ...


0

(1) Spacetime isn't all in the mind. Spacetime is just the gravitational field and it has degrees of freedom independent of your brain, so it's not all in your mind. You can't make an even happen on Tuesday just by thinking it happened on Tuesday. (2) As commented by others, you can't ride a photon. Also, the way to figure out whether something is real is ...


2

Give a physically distinguishable definition of "out there" vs. "in the mind" and we can try to discuss this further. As jinawee comments, there are no frames of reference that move with the speed of light, since the photon we "ride on" would have no speed at all by definition of a comoving reference frame, and that contradicts the constancy of the speed of ...


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 ...


0

In general it doesn't make sense to talk of curvature being only in space or only in time. The geometry of a spacetime is described by the metric. Normally we start with some distribution of matter/energy and solve the Einstein equations to calculate the metric. Alternatively you can start with the desired metric and use the Einstein equations to work out ...


0

To start with you are quoting a version of Xeno's paradoxes The conclusion to these is that the statement If you throw a rock to a tree, the rock will go half the way, then half the way, then half the way and it will keep going the half of the remaining way. Therefore, the rock will never hit the tree is absurd,, and patently wrong since the rock ...


1

First off, I'm not entirely sure of what you are asking, or what you are thinking of as curvatur. There are certainly coordinate systems which are non-euclidean that are not considered to be "curved." For instance standard cylindrical coordinates have zero Riemann Curvature, but they are "curvy looking." My take though is that in GR you have a coordinate ...


0

Is it possible to derive Lorentz transformation equation without Einstein's postulates? Yes, I did it myself. I noticed that there were flaws within the human perception of motion, meaning flaws within that which is acquired via the use of the eye in real-time. Despite having no education in physics, I proceeded to analyze motion to surpass the limited ...


3

At some time, you need physical postulates. For instance, suppose these two possible transformations applying to the infinitesimal space-time components $dt$ and $dz$, between a frame $R$, and an other frame $R'$ moving at a velocity $v_z=v$ relatively to $R$ : $$\begin{pmatrix} dt'\\dz'\end{pmatrix} = \begin{pmatrix} \cos \lambda & \sin ...


2

The "Mexican Hat Potential" (although now more politically correctly called the "Champagne Bottle Potential" after the punt at the base) is the potential energy curve for the vacuum expectation value (VEV) of the Higgs field. Think of the blue dot as being "the vacuum", and the radial direction as turning up the strength of a background field that permeates ...


0

Conventional theory calls it spacetime, which I would assume refers to an unidentified amount of space over an unidentified amount of time but both distance and time are measurements of properties of matter and are dependent upon relative matter, example. Time is the measurement of relative movement, thedistance the sun can travel in a second is different ...



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