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md65536

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Posts posted by md65536

  1. 1 hour ago, MigL said:

    That is essentially correct, and depends mostly on the model being applied.
    A classical point particle has no expectation of decay.
    A quantum particle, which can decay, cannot be localized to a point, because of e the Heisenberg Uncertainty Principle, and the fact that, in QFT, the particle is simply a manifestation of its field.

    Based on context and the forum we're in, the model must be a relativistic one. The quantum argument sounds reasonable but you can't make that claim about a gravitational singularity without a theory of quantum gravity.

     

    1 hour ago, MigL said:

    So what exactly would cause the transition to expansion/inflation ?

    I don't see how lack of a clear cause is a useful argument. If you use that reasoning, you can claim that spontaneous particle decay can't happen at all.

     

    1 hour ago, MigL said:

    The actual universe is believed to have had a finite initial size, which was subject to quantum fluctuations, and may have initiated its expansion/inflation and subsequent structure.

    Yes, it seems accepted theory is moving away from the idea of an initial singularity. My limited understanding is that the singularity is considered speculative, shown to be not necessary in some theories, and not possible in others. However the issue isn't settled because to do so would require a theory of quantum gravity. Therefore making claims as if it's settled, is speculation only. I haven't followed OP's arguments, I'm only addressing yours.

  2. On 1/17/2022 at 5:12 AM, Genady said:

    It might be easier to understand how it works by considering it in the vehicle's reference frame at the moment when it moves with the wind at the wind's speed.

    At this moment, in the vehicle's RF, there is no wind, the air stands still, and the ground moves under the vehicle backward. This movement of the ground rotates vehicle's wheels. The rotating wheels rotate the propeller. Propeller pushes the air backward and the vehicle forward. This accelerates the vehicle and it starts moving relative to air.

    In the ground RF, it starts moving faster than wind.

    I think this is the key to understanding it. I also think most people's approach is not best, whereby they imagine a contraption and explain if or how it works. If instead you ask yourself, given that the air is still and the ground is moving at a constant rate relative to it, is it possible to extract usable energy from that? It's obviously "yes". It's obvious that it could be done without breaking the laws of physics. Then other misconceptions easily fall away too. How much energy can be extracted? Now what swansont said is obvious, you would want a bigger propeller to extract more energy (the more you let the ground pull, the more you must push against the air). It's obvious that the moving ground could provide enough energy to overcome friction in a well-engineered device. It's obvious you wouldn't want a weightless vehicle, if you need a downward force against the ground to capture energy from its motion.

    Then, "How might that energy be turned into thrust, and does the device in the videos etc. conceivably do that?" is easier to think about.

  3. On 1/16/2022 at 9:51 AM, exchemist said:

    Hmm, do you mean that a glass prism gains mass if you shine a light through it?

    On 1/16/2022 at 9:54 AM, Genady said:

    No, I just mean mirrors. I take a box with internal walls being mirrors, let light in, say, through a little opening. Light just bounces inside from mirror to mirror (we can close the opening to make sure it doesn't escape). The mass of the box increased.

    I don't think the light has to be confined, and a system consisting of a glass prism with light shining through it should have more mass than just the prism.

    As a thought experiment, consider a massive particle at rest, and a photon moving with +x velocity. The photon has no mass, but considering the two particles as one system, this is not its rest frame. In the system's rest frame, the massive particle has some -x momentum balancing the photon's momentum. As a system, the particles' kinetic energy contributes to the system's rest mass.

    Likewise the prism+light's rest frame would be different from the prism's rest frame. I don't know if this is meaningful in general, since spacetime curvature depends on how the mass is distributed, and I can't imagine how to describe the effects of unconfined photons. However there are cases where it is meaningful, such as with a "kugelblitz", a black hole created by a dense concentration of light energy for example.

  4. 23 hours ago, MigL said:

    it expends the same amount of energy climbing out of a gravitational well irrespective of path taken, but depending only on the relative heights in the gravity well.

    Yes, but gravitational potential is a Newtonian thing, and that applies (always) in a Newtonian analysis.

    I was going to use gravity assist / planet flyby as an example of how an object can climb out of a gravity well using less energy, in a changing gravitational field. However, in Newtonian physics, the planet's gravitational force acting on the object equals the force of the object acting on the planet, and the object still uses the same energy to climb, it just gets it from the planet. So it's not the case that a dynamic system alone breaks gravitational potential's path independence.

    GR is a different system, and I don't understand where and how the analogy to gravitational potential fails. But for example, I read that if you separate two masses, the GR analog to gravitational potential depends on if the masses are spinning, but the Newtonian gravitational potential doesn't.

  5. On 12/1/2021 at 6:23 PM, Markus Hanke said:

     the volume implied by an entire bundle (congruence?) of such world lines should also be something everyone agrees on.

    A light-like path has a geometric length of zero, so all events on a given light cone should have a geometric (hyper)volume of zero. The interior of the cone would have positive volume (by choice of convention) or a time-like volume. The elsewhere would have negative or spacelike volume.

    The union of multiple light cones should have zero volume.* So for example if you have a light on the train, and turn it on at the beginning of the train's "life" and off at the end, then the geometric volume of all parts of the train that are lit over its entire life, is 0. If you consider only the lit part of the train (chop off everything outside the "light on" event's future light cone, and everything inside the "light off" event's future light cone), the train's entire existence has 0 geometric volume.

    Am I thinking about that reasonably? If so, I'm not sure if an invariant volume would make sense. It seems like a long-lived train, treated as a bunch of time-like world lines, should have a time-like volume.

    Or could you add up all the time-like world lines and get a different volume?

     

    * Or... did I make a mistake here? Maybe you can't just add up two light cones, because there are space-like intervals between events on the different cones, but then there are also time-like ones... Now I really don't see what a geometric volume could possibly mean.

  6. On 12/2/2021 at 3:25 PM, Markus Hanke said:

    How so? Time dilation between two points would be a time-dependent function rather than a single value, since all of spacetime here is filled with gravitational radiation.

    I mean between two events. I'm reasoning that if two clocks are identical except for their histories (basically, same place, time, and speed), they must tick at the same rate, and have the same time dilation factor relative to some distant clock. Therefore the time dilation factor between two clocks can't depend on "how the clocks got there" (I'm generalizing), yet a calculation of something representing gravitational potential, could.

     

    13 hours ago, studiot said:

    In your pursuit of gravitational potential are you interested in the application of 'the virial theorem' to cosmology ?

    [...] If you want them the derivation is about 10 pages and also involves derivatives (or jacobians) of the Einstein equation and its solutions.

    I've never heard of the virial theorem. It looks not basic enough for me. I should look at the derivation but I'd probably give up after getting lost at the top of page 1.

     

  7. 18 hours ago, Markus Hanke said:

    As such it isn’t possible to assign a single unique value that signifies gravitational potential to any point in that spacetime.

    But there is a unique single value gravitational time dilation factor between two points (in your example at least). Elsewhere on the web I see that gravitational potential represents the metric only as an analogy. Then the resolution might be that "gravitational time dilation is determined by the metric," while it's not always applicable that "gravitational time dilation is determined by gravitational potential"?

  8. On 9/18/2021 at 2:23 AM, Markus Hanke said:

    Correct - but with the caveat that the concept of ‘gravitational potential’ can only be meaningfully defined in certain highly symmetric spacetimes, such as Schwarzschild. It is not a generally applicable concept.

    Resurrecting this idea, that I never ended up wrapping my head around...

    Say we use a mountain as an analogy for an arbitrary spacetime. There's a clock at the top. Two travellers each transport a clock down the mountain along different routes, and meet at the bottom. There, they generally find their clocks have aged differently, but the two clocks, together at relative rest, are now ticking at the same rate. Their clocks tick at a different rate from the clock at the top, but of course the two clocks at the bottom share the same time dilation factor relative to the one at the top. Therefore there must be a scalar number that relates the two locations, that is independent of any differences in how spacetime is curved along the different paths between the two.

    In this analogy, "height" works as that single scalar, and gravitational potential is meaningful. Is there another such scalar that relates two locations in an arbitrary spacetime, or is it just the "time dilation factor", and that factor isn't completely determined by any other scalar factor alone? Or, is it that gravitational potential loses meaning only where there aren't worldlines between the two locations?

     

     

    Or to ask in a different way, if you have two particles in freefall with different velocities, that pass through some one event and later pass at some second event, is gravitational potential certainly meaningful along their respective freefall paths, and if so is it the same along both paths, no matter how asymmetric the spacetime is?

  9. 1 hour ago, Janus said:

    10,000 meters in the track frame.  If the lightning strikes occur 100 m apart in the train frame, then scorch marks they leave on the tracks are 100 m apart as measured from the train frame.  Since the train measures the track as being length contracted by the same factor ( 1/100) as the track frame measures the train, then the proper distance between the scorch marks as measured from the track frame is 100m x 100 = 10,000 m.

    Of course this means that the rear of the train ( being only 1 m long as measured from the tracks) reaches the point on the tracks where it and the tracks are hit by lightning while the front of the train is still 9,999 m short of where it will be struck by lightning, making the lightning strikes non-simultaneous in the track frame.

    I agree. Interesting that you reasoned it out right from the start, and transferred the events from the train to the tracks, at rest in their frame. Was that essential to the reasoning, or just because that's what the question asked? (If I could redo the question, I'd make them ships in space without the tracks, but would that make the question harder to reason?)

    Reciprocality should become pretty intuitive given the first postulate, it seems like a major prerequisite to understanding relativistic effects.

     

  10. 3 hours ago, Country Boy said:

    You said that the train's "rest length" is 100 m.   Then in the train's frame of reference the two lightening strikes are 100 m apart.  Of course, in the track's frame of reference, the two lightening strikes are 1 m apart.

    [...] I don't know what you mean by "abstract distance".  Any distance, pretty much by definition, can be measured, as well by a meter stick as any other way.

    Yes, they're 100 m apart in the train's frame. The strikes / tunnel can't be 1 m in the track frame unless that 1 m expands to 100 m in the train's frame, which it doesn't.

    Yes, I used 'abstract' incorrectly. It's the added object (like a ruler, train platform, extra tunnel etc.), used to conceptualize the distance, that's abstract.

     

  11. 4 hours ago, 34student said:

    Is there one or more sizes of train in the frozen 3d universe at time = t* 

    distance-between-lines.png.517f10eef1c5930e4411f497148d4460.png

    What is the length of a line segment that connects line A at point p, to line B? Is it one or more of a,b,c,d,e, or something else?

    If line A represented the world line of the front of a train, and B the world line of the back of the train, what is the length of the train?

    This doesn't even illustrate length contraction or the rules of relativity. I think you're missing some basic geometry in what you're asking.

     

  12. 5 hours ago, 34student said:

    The way I am thinking about all of this is that t' and t are on one timeline since the universe would only have 1 dimension of time.  So t' is going to intersect with some t.  Do you believe that t' is inside the interval t, where t is the from the beginning of the year 2050 to the year 2100, from the OP example?

    "One timeline" is meaningless to me. t' inside t is also meaningless... you're effectively asking if the time measured by one clock is inside the time measured by another clock. But you could say that if Bob leaves the train at 2050 and returns to it at 2100, its world line between those events is within the future light cone of the train in 2050, and the past light cone in 2100, and that's what you want: all observers agree that Bob's trip happened after the 2050 event and before the 2100 event.

    However, if Bob didn't start/end near the train and was always far enough away, that's not true for all observers. As well, Bob's cousin Babs, who suppose shares Bob's inertial frame and clock for an inertial part of Bob's trip, but was in the Andromeda galaxy during proper time interval t', is completely outside the light cones mentioned, so in that sense t' is not "inside" t, and far away events occurring at proper time t' can be before, during, or after (depending on frame of reference) the t interval from 2050 to 2100.

     

     

    Yes, the block universe has one time dimension, but you can choose it in different ways (as MigL said, "You can have many different 'foliations' of the 4D hypercube, and all are equally valid.") If you have the block universe in coordinates so that the front of the train is always at the same location with one x value, its world line is a straight line aligned with the T axis. But you can rotate (hyperbolicly) the block universe so that Bob's world line is now aligned with the new T' axis, and the train front's world line span different x' values.

    This doesn't imply multiple universes, blocks, trains etc. any more than someone in Russia having a different vector pointing "up" than someone in Argentina, implies that there are multiple Earths. Say they each have a y-axis that points "up", you have one Earth described using 2 different sets of coordinates, each more appropriate than the other to some observer.

  13. I was thinking about this as an example for another thread but thought it would only add confusion.

     

    Say you have a train with proper length 100 m, traveling so fast that it contracts to 1 m according to the tracks' reference frame.

    Suppose that in the train's frame, lightning strikes the front and back of the train simultaneously. How far apart are the lightning strikes on the track?

     

    Can anyone answer this with just a few seconds thought? I can't, I have to figure out the details and calculations, but if I ask a different question...

    Spoiler

    Suppose the train goes through a tunnel and exactly fits inside it, in the train's frame. How long is the tunnel in the tracks' frame?

     

    They're the same question, but only one seems intuitively obvious.

    Spoiler

    Is it a common to replace an abstract distance with a ruler, in thinking about things like this? Or is the first question intuitive with enough experience?

     

  14. 13 hours ago, 34student said:

    Yes, you understand my question.  Now are there also world lines from 2 particles that are 100 meters apart, as measured from an observer on the train?

    There are events on the those same 2 world lines that are 100 m apart to that observer, yes. They're on the same world lines, but they're not the same pair of events that are 1 m apart in Bob's frame. The two observers use different time coordinates, and 2 events at the same t and 100 m apart in the train's frame, don't have the same t' value in Bob's frame. The 1 m length of the train that Bob measures is between 2 events on the respective world lines with the same t' value. This is "relativity of simultaneity."

    Using world lines instead of lengths isn't going to change the details of the simpler examples you're using them to represent.

    10 hours ago, Markus Hanke said:

    The very title of the thread already gave it away right from the start, but I had been hoping that explaining the theory plus listing experimental evidence might have had some effect at least. Sadly though, at this point the best term I can think of to describe this thread is ‘sealioning’.

    I suppose we persist because we expect a response like "That's something I don't get, let me try to understand that first" instead of "What if I ignore all that and ask the same question in different words?" Block universe, world lines... it's like expecting to find some aspect of relativity for which the rules of relativity don't apply.

  15. 12 minutes ago, studiot said:

    But I don't think the OP means the same sort of distance as you do, since he is measuring in metres.

    I did mean the same thing, but failed to state it. I should have said I meant the spatial distance between two events at the same time in a particular frame of reference. Did I imply the invariant length of a spacetime interval?

    ...thus proving my point that you have to specify these details for things to make sense to others!

  16. 3 hours ago, jamesfairclear said:

    One could envisage an experiment whereby a light source is set in motion at a constant speed S and then illuminated at a distance D from a relatively stationary detector. A clock at the detector measures the time it takes the Doppler redshifted light to arrive from distance D in order to establish its speed.

    That doesn't work unless you know the time at the light source, and you can't measure that from the detector. You theoretically can't measure the one-way speed of light, but you don't have to measure it since it is by definition equal to c. You can measure the 2-way timing of light, and find the one-way speed because literally by definition, the time that it takes for the light to go 1 way is the same as the time it takes to go the other way.

    You can however confirm that light from a distance D takes the same time regardless of the motion of the light source. For example, if you have 2 sources moving in opposite directions, and a signal from each of them when they're at the same location, you can verify that the 2 signals arrive at the same time. You don't have to know what time they're sent at, if all you care about is that they were sent at the same time, and you can make sure that happens by sending them from the same location.

  17. 35 minutes ago, 34student said:

    Since the particles are 1 meter apart and they travel along world lines through time, then doesn't that imply that their world lines are also 1 meter apart?

    Your line of questions shows you're not going to understand the answers. Why don't you start with simpler concepts first and understand them before talking about world lines?

    The world line of a particle is made up of all the events in the particle's entire lifetime. You're asking for the distance between two arbitrary lines. I think what you're really asking for is the distance between particular pairs of events on those world lines, but you're not specifying that unambiguously.

    If you're using coordinates where Bob's world line remains fixed at one x,y,z location and only varies in T, then (based on the situation you've implied), the distance between a given event at time T1 on the world line of the front of the train, and an event at the same time T1 on the world line of the back of the train, will be 1 m apart. If you use other coordinates, you'll get other answers.

    If you're talking about measurements in the block universe, you should specify what coordinates you're using. If you're talking about observations, you should make it clear what frame of reference you're using. If you're measuring the distance between 2 objects over their entire lifetimes (ie. world line) you should make it clear what time you're talking about. And if you're talking about a single moment across a distance, to even make sense of that requires the set of coordinates or frame of reference! If you want specific answers, your questions have to make sense, and they haven't been.

     

  18. 25 minutes ago, 34student said:

    So if there are 10 cars to the train, are you saying that there actually are 20 cars?

    Could you please stop taking what is said and twisting it to fit your existing misunderstanding? It's been repeated ad nauseam that that there's only one train.

    2 hours ago, 34student said:

    Now here is my question that will either put my issue to rest for me or keep me wondering.  If the particle is at x1 for Bob, and x2 for people on Earth, does the particle necessarily have to go through x1 and x2 (not necessarily in this sequence)?

    No, because those are 2 different coordinate systems. For example, the front of the train can be at rest at x2=0 for the coordinate system of an observer at the front of the train, while Bob might use a coordinate system where his ship is at the origin and the location of the front of the train is x1=several light years and changing. If the front of the train enters a tunnel, that's an event. Everyone agrees that the location of the front of the train coincides with the location of the entrance of the tunnel when it enters, but that could be at x2=0 and x1=several light years. Though it might make more sense with all the other basic stuff about relativity that I'm sure you've read, if you called them x and x' to denote that they're different coordinate systems.

  19. 25 minutes ago, 34student said:

    That is what I thought, and this is why I am so confused.

    Going back to the example in my OP, let's think about a particle sitting at one end of the train.  The train lies on the x axis.  The particle has one "String"/world line for Bob and another for Earth observers, (and possible an infinite more creating a plane).

    Which world line is real, or do they both exist?  If both particle locations exist, why can't one of the two observers detect both particles?    

    Did none of the rest of what I wrote make sense?

    The particle has only one world line. The world line is the events (the x and t locations) that the particle passes through over its lifetime. The world line is a fixed set of events, but the x and t values of those events change if you rotate it into other coordinate systems representing other observers.

    For example, put a stick on a grid with an x and t axis. If you align it with the t axis, it has the same x value at different t, representing the world line of a particle at rest. If you rotate the grid, the stick stays the same but now it has different x at different t, representing a different observer, for which the particle is moving.

    This is an oversimplified analogy and it uses the wrong rotation, so don't draw too many conclusions from it. If you rotate the stick or grid, the stick's x and t components change, but the length of the stick stays the same. It's the hypotenuse in the Pythagorean theorem r^2 = x^2 + t^2. With the correct hyperbolic rotation, s^2 = x^2 - t^2 stays the same.

  20. 11 hours ago, 34student said:

    I always thought that the past was one 4 dimensional static block, literally a block of static particles that would look like like strings because of the dimension of time.

    Sure, that would be a block of events, and the "strings" are world lines of particles.

    Imagine you have a block of say wood, and you draw a small line on it to represent a world line. You can rotate the block in your hands, but the shape and length of the line remains invariant. Say that you rotate it through a fixed grid of coordinates in a room. Using just 2 dimensions for simplicity, you can make the line align with the x-axis, or the y-axis, or anything in between. By rotating it, you can change how long the line is in the x-dimension and how long it is in the y-dimension, without changing its length.

    But the block universe also has a time dimension, so instead of x and y, imagine it's t and x. The line could be a function x(t) representing how far x a particle moves in time t in a particular set of coordinates, and you get different x-lengths in different coordinates just by rotating the block.

     

    In this analogy the rotation is a spherical rotation which keeps r^2 = x^2 + y^2 invariant as you rotate it. With spacetime, the rotation is hyperbolic, which instead keeps s^2 = x^2 - t^2 invariant as you rotate it. So you can't just turn it upside down and reverse time etc.

  21. 1 hour ago, MigL said:

    The 'Block' Universe model is essentially devoid of time, as past, present and future are all present in the 'Block'. [...]

    The worldline of an event does not move; it is already there.

    Do you mean worldline of an object? An event is a single point in spacetime (and in the "block") and many worldlines can pass through it.

    Worldlines still exist in the block, and one's proper time is an invariant length of the world line. Different coordinate times can be defined (including just using T to represent time) and the coordinate times between distant events can be calculated in the block. I don't understand what you mean by it being "devoid of time", since all the measures of time are still there. Some philosophical "flow or time" or whatever might be taken out, but time in SR and GR is the measurement, not the concept.

    6 minutes ago, 34student said:

    Bob and Earth begin with the same t value.  When Bob returns, his t value is the same as Earth's t value when t was 2051.  For some of that year, according to Bob's clock, the train was 1 meter.  But from 2050 to 2051 on Earth, the train was never 1 meter.    

    Where's the problem? You're using coordinate time t to be the time in Earth's frame. You're stating that the length of the train is relative, and depends on the observer (ie. reference frame). That agrees with observation. That agrees with relativity. Nothing there implies illusion.

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