Scenario in an attempt to understand relativity

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In summary, the conversation is about the measurement of the speed of light and how it remains constant for all observers, regardless of their relative speeds. The concept of time dilation and length contraction is discussed in relation to a scenario where a photon is emitted and travels one light year before being absorbed by an object. The conversation also mentions the difficulty of using a single photon for measurement due to its inability to be observed by multiple observers.
  • #1
CosmicVoyager
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Greetings,

I am trying to figure out how that can be that everyone can measure all light from any source to be the same speed no matter the speed of the measurer or the source. It seems that the photons would have to be in different places depending on where the person doing the measuring is and at what speed they are traveling.

What would happen in this scenario:

If a year after a photon is emitted, there is an object, which is stationary relative to the source, a light year away in the path of the photon, then the photon will be there and be absorbed. And the light will seem to have taken one year to travel one light year. Correct?

Now, if instead, a year after the photon is emitted (according to clocks at the source and first object), there is an object which is moving (relative to the source and first object) and therefore experiencing time dilation (relative to the source and first object), in the same place as the first object, will the photon be there and be absorbed? Since clocks would be running slower for that object, it would measure the light to have taken less time to travel the light year. So it seems that it would *not* detect the photon. It seems that the second object would have to be in a different location to detect the same photon that the first object would. It seems that whether the photon is at a location depends on the relative speed of an object that would be there to detect it.

Thanks
 
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  • #2
CosmicVoyager said:
Since clocks would be running slower for that object, it would measure the light to have taken less time to travel the light year. So it seems that it would *not* detect the photon. It seems that the second object would have to be in a different location to detect the same photon that the first object would.

The distance covered by the photon is Lorentz-contracted in the frame of this object.
 
  • #3
When we talk about everyone measuring the speed of the same light burst (I'd rather talk about a bunch of photons because, as you pointed out, if you're talking about a single photon, as soon as it gets absorbed by one observer, it ceases to exist and cannot therefore be observered by anyone else), we are always talking about a round trip (another thing a single photon cannot do) involving reflection from a mirror a measured distance away. Each observer will have their own mirror and so there are two different reflections. The time it takes to go from an observer to his mirror and back to the observer is what is used for that observer to calculate the round trip speed of light. A second observer moving with respect to the first will do the same thing with a different portion of the light and because his ruler is contracted and his clock is running slower will calculate the same speed for the round trip of the light.
 
  • #4
bcrowell said:
The distance covered by the photon is Lorentz-contracted in the frame of this object.

ghwellsjr said:
...and because his ruler is contracted and his clock is running slower will calculate the same speed for the round trip of the light.

Isn't Lorentz contraction parallel to the direction of movement?

I mean for the second object to be moving perpendicular to the path of the photon from the source, and to cross the path at the location of the first object when the first object's clock would indicate one year had elapsed. So the second object would be at the same location as the first at the same time (according to the first's clock) and without Lorentz-contraction in the direction of the photon source.
 
  • #5
CosmicVoyager said:
I mean for the second object to be moving perpendicular to the path of the photon from the source[...]

OK, in that case have you tried writing out the Lorentz transformation in 3+1 dimensions and checking that it comes out consistent? The Lorentz transformation is essentially designed so that it will give consistency for the speed of light.
 
  • #6
bcrowell said:
OK, in that case have you tried writing out the Lorentz transformation in 3+1 dimensions and checking that it comes out consistent? The Lorentz transformation is essentially designed so that it will give consistency for the speed of light.

I don't know how. lol If the second object would still detect the same photon, could someone explain in english how that can be :-) For example, if the second object were moving parallel, the reason would be that length is contracted between the object an the source. What is the reason if it is moving perpendicular?
 
  • #7
You're conflating many different concepts here which makes it very difficult to address your concerns. I think what you want to know is how time dilation and length contraction work to cause a moving observer to get the same answer for the speed of light when the light is traveling either perpendicular or parallel to his direction of motion since there's no length contraction in the first case but there is length contraction in the latter case. Is that correct? But I'm not sure you understand either of these two cases, is that correct?

You're also talking about the light starting at one source where there is no observer, and traveling for one light year before it arrives in the vicinity of an observer who is stationary to the light source and another observer who is moving with respect to the light source. And you want to use the time that it takes for the entire trip in your measurement. And you want to use a single photon. And you want the second moving observer to travel perpendicular to the path of the photon. All this makes for a very difficult, if not impossible scenario to discuss. I'm not even sure how to configure what you have in mind.

I already mentioned the problems of using a single photon:
1) A single photon cannot be observed by two different observers.
2) A single photon can only go in one direction.
So can we please not talk about a single photon and instead talk about a flash of light?

I already mentioned the fact that a measurement of the speed of light must involve a round trip and the observer has to be located at the start of the trip and at the end of the trip. So your idea of light starting a light-year away where there is no observer and using that distance and the time it takes for light to travel that distance is not a measurement. To make a measurement of speed, you have to have a ruler and a stop watch and you calculate the speed by dividing the total distance by the total time. These are ideas the Einstein discussed in his 1905 paper where he introduced Special Relativity to the world. We would be wise to follow his example.

So can we please change your scenario into something more conventional? I suggest that you consider a very popular Special Relativity issue, which is sometimes called a paradox. It goes like this:

We have two observers, I, George, will be the first one and we'll assume that I'm stationary and I have a flash bulb that I have arranged to be energized when you, the CosmicVoyager traveling toward me in a straight line at half the speed of light arrive at my location. You carry a stop watch, as do I, which we both start at the moment of the flash. You continue on without stopping or slowing down. The very bright flash of light will expand outward from its starting point in a perfect sphere getting bigger at the speed of light. According to Special Relativity, I will measure myself to be in the exact center of the expanding sphere of light. That makes sense, doesn't it, since I set off the light and I'm not moving? But according to Special Relativity, you will also measure yourself to be in the exact center of the expanding sphere of light and that doesn't seem right, does it, because you are moving with respect to the source of the light? But would it make sense if you were the one carrying the light source and to have set it off when you arrived at my location? Maybe, but in this case, I, too, would measure myself to be in the center just like you would. And that doesn't seem right but it really doesn't matter what the speed of the source of the light is or the speed of the observers, they all will think they are in the center of the expanding sphere of light. This can only work if the speed of light is the same for all observers, do you agree with that?

So how do we observe or measure this expanding sphere of light? Well, once it has traveled away from us, we can have no awareness of its existence or its progression through space unless we place some detectors out in space to tell us when the light arrives at a given location. We could, in principle, wire up some light detectors with long wires to let us know when the light hits them but this has the disadvantage that we would have to take into account the propagation of the signal along the wire back to us. A better idea, in fact, the best idea is to place a bunch of mirrors out in space, all a constant distance away that will simply reflect the light back to us and then if we see the light arriving from all mirrors simultaneously we will know that we are in the center of the expanding sphere of light and we will stop our stopwatch when that happens and calculate the speed of light by taking twice the distance and dividing by the time.

Now it's important to realize that we each must have our own set of mirrors because you are traveling with respect to me and your mirrors must be traveling at the same speed as you are. So I take my ruler and carefully place them some constant distance from me and aimed back toward me. My mirrors will form a perfect sphere. You do the same thing with your ruler except that since you are moving, your ruler is length contracted whenever it is parallel to the direction of your motion. But your ruler is the same length as mine when it is perpendicular to your direction of motion and somewhere in between for other angles. So your mirrors will not form a perfect sphere like mine will but rather a somewhat flattened sphere. However, to you it looks like a perfect sphere because you, too, are flattened in the same way.

Now what happens when we carry out out test? Well it's a little difficult to describe in words so I have created a little animation that depicts what happens:



In this video, I, the stationary observer, am depicted in green and you, the moving observer, are depicted in red. Our mirrors are in yellow. The outgoing expanding sphere of light is depicted in blue and the collapsing sphere of light reflecting off my mirrors is shown in green while the collapsing sphere of light reflecting off your mirrors is shown in red. Now you will note the shape of my mirrors form a section through a perfect sphere whereas the shape of your mirrors is compressed along the direction of your motion.

Now if you follow the progression of the light as it is expanding, it forms a perfect circle and hits all my mirrors at the same time which forms a perfect shrinking circle that collapses on me from all directions simultaneously, taking a particular amount of time which when divided into the total distance yields the correct measure of the speed of light.

Now what happens with your mirrors? It turns out that the light does not hit all your mirrors at the same time but what does happen is they create a perfect shrinking sphere of light but repositioned to collapse on you at just the right time as required by Special Relativity according to time dilation (a lengthening of time).

It's important to realize that what we see of the progression of light in the animation is not available to us as observers in the animation. We, as observers in the video only know about the beginning of the flash and the separate returns of the reflected flashes off our individual set of mirrors.

Let me know if this helps you with your question or if you have any more questions.
 
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  • #8
That is awesome! Thanks :-)

I will think about it some more and see if it raises any questions. I took a conceptual basic physics class which focused on understanding. I wish there was a conceptual relativity class, and a conceptual quantum physics class.

We know that time dilation is more than a technique to make things work out. We have actually measured it with pairs of high precision clocks. Is there a way to measure length contraction to know objects are actually getting thinner? Since density is increasing, it's gravity should be affected. You could pass in front or behind it closer to it's center since it is narrower and experience stronger gravity.
 
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  • #9
CosmicVoyager said:
That is awesome! Thanks :-)

I will think about it some more and see if it raises any questions. I took a conceptual basic physics class which focused on understanding. I wish there was a conceptual relativity class, and a conceptual quantum physics class.

We know that time dilation is more than a technique to make things work out. We have actually measured it with pairs of high precision clocks. Is there a way to measure length contraction to know objects are actually getting thinner? Since density is increasing, it's gravity should be affected. You could pass in front or behind it closer to it's center since it is narrower and experience stronger gravity.
Measuring time dilation requires that length contraction must also be happening, or else it would be possible to build a clock that would keep different time depending on its orientation with respect to the direction of motion, don't you think?

Also, keep in mind that a clock is accumulating time dilation which is the reason why we can see a difference between the clock that took a trip and the one that remained stationary. Once the two clocks are brought back together, there is no more difference in time dilation for them, as they tick at the same rate. If we took a metronome (which is the ticking portion of the clock without the accumulator) on a trip and left one at home, we would not be able to demonstrate time dilation because whenever we brought them back together for comparison, they would be ticking at the same rate.

If we could devise a similar instrument, like an odometer, that would accumulate length contraction of the distance traveled, then we would see that taking two such instruments on the same path at different speeds would measure different length accumulations. Actually, we can build such instruments but they have no where near the precision, stability and accuracy to demostrate length contraction, but maybe some day we will.

But to me, the fact that traveling clocks demonstrate time dilation without regard to their orientation is proof enough that length contraction is also being demonstrated, otherwise, it would be possible to devise a clock that would be sensitive to its orientation and we could take two or more of them on the same trip and they would keep accumulate different times.
 
  • #10
Okay, I have run into a problem with the idea that objects get narrower the faster they move.

If I were to measure out the distances between my mirrors when I am stationary to you, and I and all of the mirrors were to accelerate together, then they should still be arranged in a circle because as the mirrors narrow, the space between them increases since they are not connected.

This also got me to thinking more about what is happening when an object narrows. Objects are made up of smaller objects, and it is actually the smaller objects that are narrowing, and when when they do, the space between them increases. The length of the larger object would stay the same if it were not for the forces binding solids together, and the object should be torn apart if accelerated quickly enough. The edges of the object would undergo the most strain since they would move a longer distance toward the center. It seems like we should be able to measure this.
 
  • #11
CosmicVoyager said:
Okay, I have run into a problem with the idea that objects get narrower the faster they move.

If I were to measure out the distances between my mirrors when I am stationary to you, and I and all of the mirrors were to accelerate together, then they should still be arranged in a circle because as the mirrors narrow, the space between them increases since they are not connected.

This also got me to thinking more about what is happening when an object narrows. Objects are made up of smaller objects, and it is actually the smaller objects that are narrowing, and when when they do, the space between them increases. The length of the larger object would stay the same if it were not for the forces binding solids together, and the object should be torn apart if accelerated quickly enough. The edges of the object would undergo the most strain since they would move a longer distance toward the center. It seems like we should be able to measure this.

No. Length contraction is not something that "physically" acts on objects. It means that reference frames in motion with respect to each other measure the length differently. In other words, if there are two points in space that are 1 meter apart according to you, for someone traveling parallel to the line joining them, these two points will be closer together, regardless of the fact that there is no physical connection between those points or even if there is any physical objects at those point.

So in your above examples, the distances between the discreet objects also length contract.
 
  • #12
CosmicVoyager said:
Okay, I have run into a problem with the idea that objects get narrower the faster they move.

If I were to measure out the distances between my mirrors when I am stationary to you, and I and all of the mirrors were to accelerate together, then they should still be arranged in a circle because as the mirrors narrow, the space between them increases since they are not connected.

This also got me to thinking more about what is happening when an object narrows. Objects are made up of smaller objects, and it is actually the smaller objects that are narrowing, and when when they do, the space between them increases. The length of the larger object would stay the same if it were not for the forces binding solids together, and the object should be torn apart if accelerated quickly enough. The edges of the object would undergo the most strain since they would move a longer distance toward the center. It seems like we should be able to measure this.
You are correct when you say if the mirrors accelerate together, you mean that you put individual rockets on each mirror and accelerate each of them with no rigid connectors between them but if you mean they are fastened to some kind of structure and you have only one rocket that accelerates the entire structure together, then the mirrors will move closer together.

And you are correct when you talk about an "object should be torn apart if accelerated quickly enough". Yes, yes, yes, but when we discuss these thought problems in relativity, we ignore all these issues that would bring us down to reality because there are so many of them and we can't do anything about them anyway. So we pretend. The only things we can actually accelerate to these speeds are atomic particles and all experiments that can and have been done support the conclusions of special and general relativity.
 
  • #13
Janus said:
No. Length contraction is not something that "physically" acts on objects. It means that reference frames in motion with respect to each other measure the length differently. In other words, if there are two points in space that are 1 meter apart according to you, for someone traveling parallel to the line joining them, these two points will be closer together, regardless of the fact that there is no physical connection between those points or even if there is any physical objects at those point.

So in your above examples, the distances between the discreet objects also length contract.

"Length contraction is not something that "physically" acts on objects."

Okay, this is what I was afraid of. It seems to me this "length contraction" idea is just a convenient mathematical correction to compensate for something we have no explanation for, made up so that things will work out in calculations so that it can be predicted how things will *appear* in different circumstances. It is not really happening. Rulers are not contracting. And space is certainly not expanding and contracting based on how fast an object is moving. So it is extremely misleading to say objects flatten the faster they go. The correct answer for how it is that the speed of light can be measured to be the same regardless of one's speed is "No one knows. We only know how to calculate what the results of measurements will be."
 
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  • #14
CosmicVoyager said:
"Length contraction is not something that "physically" acts on objects."

Okay, this is what I was afraid of. It seems to me this "length contraction" idea is just a convenient mathematical correction to compensate for something we have no explanation for, made up so that things will work out in calculations so that it can be predicted how things will *appear* in different circumstances. It is not really happening. Rulers are not contracting. And space is certainly not expanding and contracting based on how fast an object is moving. So it is extremely misleading to say objects flatten the faster they go. The correct answer for how it is that the speed of light can be measured to be the same regardless of one's speed is "No one knows. We only know how to calculate what the results of measurements will be."

Suppose you have a cube and you shine a light on it, and look at its shadow on a screen. If you orient it right, its shadow will be a square. If you rotate the light and the screen properly, you can make the shadow look like a hexagon. When you say "it is extremely misleading to say objects flatten the faster they go.", that is like saying "it is extremely misleading to say a square turns into a hexagon when you rotate the light and screen".

The square and hexagon are only 2-dimensional shadows of the real thing - the cube. What is the true shape of a cube? Is it square or hexagonal? Neither, its a 3-dimensional object. In the theory of relativity, when you talk about the length of an object, you are talking about a shadow of a 4-dimensional object that exists in space and time. Different inertial frames view this 4 dimensional object in different ways. They measure different lengths of the object, different shadows. When you are at rest with respect to the object, you see a shadow which is longer than any other shadow, its called the "rest length".

Just like when you look at the shadow of a cube, the square shadow is special - no other shadow has a smaller area. But so what? Basically, Einstein realized that its all about the cube, not about its shadows. He developed the geometry and physics of 4-dimensional spacetime, and explained how different inertial frames saw the shadows that resulted. This is more than saying that he just came up with a bunch of equations that worked and had no idea what they meant.
 
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  • #15
Rap said:
Suppose you have a cube and you shine a light on it, and look at its shadow on a screen. If you orient it right, its shadow will be a square. If you rotate the light and the screen properly, you can make the shadow look like a hexagon. When you say "it is extremely misleading to say objects flatten the faster they go.", that is like saying "it is extremely misleading to say a square turns into a hexagon when you rotate the light and screen".

The square and hexagon are only 2-dimensional shadows of the real thing - the cube. Is the cube a square or a hexagon? Neither, its a 3-dimensional object. When you talk about the length of an object, you are talking about a shadow of a 4-dimensional object. Different inertial frames view this 4 dimensional object in different ways. They measure different lengths of the object, different shadows. When you are at rest with respect to the object, you see a shadow which is longer than any other shadow, its called the "rest length".

Okay, this sounds promising :-) So you are saying there *is* a way of reconciling the apparent contradictions. Could you or anyone explain the idea in detail like ghwellsjr did with his scenario, preferably with illustrations (but anything is welcome)? ghwellsjr's explanation almost worked. I am imagining the 2d to 3d equivalent of this 3d to 4d scenario, and I don't see how one's speed would cause one to see a higher dimensional object from a different angle. My speed would not cause the object to rotate, and my speed would not move me up or down off my plane. Thanks.

*edit
I thought about this some more and realize that everything including the observer would be 4-dimensional objects. If that were true, why do we only see and move in three? Why are we confined to 3 axes?
 
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  • #16
CosmicVoyager said:
Okay, this sounds promising :-) So you are saying there *is* a way of reconciling the apparent contradictions. Could you or anyone explain the idea in detail like ghwellsjr did with his scenario, preferably with illustrations (but anything is welcome)? ghwellsjr's explanation almost worked. I am imagining the 2d to 3d equivalent of this 3d to 4d scenario, and I don't see how one's speed would cause one to see a higher dimensional object from a different angle. My speed would not cause the object to rotate, and my speed would not move me up or down off my plane. Thanks.
If my "explanation almost worked", I'd like to know where it disappointed you. What are the "apparent contradictions" that you would like reconciled?
 
  • #17
CosmicVoyager said:
Okay, this sounds promising :-) So you are saying there *is* a way of reconciling the apparent contradictions. Could you or anyone explain the idea in detail like ghwellsjr did with his scenario, preferably with illustrations (but anything is welcome)? ghwellsjr's explanation almost worked. I am imagining the 2d to 3d equivalent of this 3d to 4d scenario, and I don't see how one's speed would cause one to see a higher dimensional object from a different angle. My speed would not cause the object to rotate, and my speed would not move me up or down off my plane. Thanks.

Draw a graph, vertical axis is time in years, horizontal axis is space in light years. That's "your" space and time. That means that a light beam will be at a 45 degree angle. Now draw a line from the origin upwards and to the right, at an angle to the vertical (time) axis that is smaller than 45 degrees, so it represents a person moving slower than the speed of light. The old, classical way of looking at things (i.e. "Galilean") says that the time axis for that other person is the vertical axis and the space axis for that other person is the horizontal axis - same as it is for you. Einstein said, no, the time axis for that moving person is the slanted line, not the vertical line any more, and the space axis for that person is perpendicular to that time axis, not the horizontal axis any more. Thats how the rotation happens. There is no special space or time axis, everybody makes their own.

Draw two dots on the graph. These are events, like firecrackers going off, they have a fixed point in spacetime. You drop a perpendicular from those points to your space axis - that's the distance you see between the events. You draw a perpendicular to your time axis - that's the time you see between these events. Draw a perpendicular to the other person's space and time axes, that's the space and time intervals that they see between these events - totally different.

Now comes the hard part - spacetime is not a Euclidean space. The distance between two points in Euclidean space is the square root of x^2+y^2+z^2 no matter what your axes are, but in spacetime, the spacetime distance between two points is the square root of x^2+y^2+z^2-t^2 (x,y,z in light years, t in years) no matter what your axes are. That minus sign in front of t^2 changes things. It means that what you draw as perpendicular on your Euclidean graph paper does not represent a perpendicular in non-Euclidean spacetime. For your space and time, the perpendiculars you draw on your graph are ok, but a perpendicular to the other person's time axis does not drop below your space axis at the same angle, it goes above it by the same angle, and when you draw perpendiculars to the other persons space and time axes, they won't look perpendicular on your Euclidean piece of paper. As the other person goes faster and faster, their time axis will get closer and closer to the 45 degree line, the speed of light, and their space axis will get closer and closer to that 45 degree line as well. If you tell the other person to draw a graph of things, like you have done, they will say that the speed of light is 45 degrees on their graph too! This gives you a feel for why the speed of light is special.
 
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  • #18
ghwellsjr said:
If my "explanation almost worked", I'd like to know where it disappointed you. What are the "apparent contradictions" that you would like reconciled?

As I said above,
"If I were to measure out the distances between my mirrors when I am stationary to you, and I and all of the mirrors were to accelerate together, then they should still be arranged in a circle because as the mirrors narrow, the space between them increases since they are not connected."

To which you replied,
"You are correct when you say if the mirrors accelerate together, you mean that you put individual rockets on each mirror and accelerate each of them with no rigid connectors between them but if you mean they are fastened to some kind of structure and you have only one rocket that accelerates the entire structure together, then the mirrors will move closer together."

If I measured them out into a circle, then accelerated and they remained in a circle then they are not in the ellipse needed to make the light appear to travel at the same speed for me as it does for you.

Anyway, Janus replied saying,
"Length contraction is not something that "physically" acts on objects. It means that reference frames in motion with respect to each other measure the length differently. In other words, if there are two points in space that are 1 meter apart according to you, for someone traveling parallel to the line joining them, these two points will be closer together, regardless of the fact that there is no physical connection between those points or even if there is any physical objects at those point.

So in your above examples, the distances between the discreet objects also length contract."To which I replied,
"Okay, this is what I was afraid of. It seems to me this "length contraction" idea is just a convenient mathematical correction to compensate for something we have no explanation for, made up so that things will work out in calculations so that it can be predicted how things will *appear* in different circumstances. It is not really happening. Rulers are not contracting. And space is certainly not expanding and contracting based on how fast an object is moving. So it is extremely misleading to say objects flatten the faster they go. The correct answer for how it is that the speed of light can be measured to be the same regardless of one's speed is "No one knows. We only know how to calculate what the results of measurements will be."
 
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  • #19
Rap said:
...

I do not follow this explanation :-(

I was expecting an explanations using four physical dimensions with 4d objects like hypercubes.

I do not see how to translate it into a specific such as the one in my first post or the one ghwellsjr gave. I am wondering if this can be illustrated with the universe as a plane with 2d objects on it and other planes being time.

This just seems to be a graph of how things appear, and not an explanation for how it is that they can appear hat way, not how observers moving at different speeds could measure something (light) to be the same speed like ghwellsjr animation was.

"spacetime is not a Euclidean space. The distance between two points in Euclidean space is the square root of x^2+y^2+z^2 no matter what your axes are, but in spacetime, the spacetime distance between two points is the square root of x^2+y^2+z^2-t^2 (x,y,z in light years, t in years) no matter what your axes are."

So it really isn't distance. Time is not a physical dimension. Time is concept. I line representing time is a graph of changes in the arrangement of objects. And if you were to add a fourth axis it should add the same distance as adding a second and third do.

Also, if time were a fourth dimension that the universe was in then there are two possibilities, both of in which the above explanation does not work:

Possibility A - Everything in the universe is moving through time. The past and the future are empty. Objects could not be at a different place in time than other objects because they would disappear from the slice of time that the rest of the universe is in.

Possibility B - Objects are four dimensional and extend backward in time. They are *extremely*, if not infinitely, long and connect to each other in the past. If this were the case then we should experience all of time at the same time and not just one slice of it, since we are four dimensional objects that are everywhere in time.
 
  • #20
CosmicVoyager said:
"spacetime is not a Euclidean space. The distance between two points in Euclidean space is the square root of x^2+y^2+z^2 no matter what your axes are, but in spacetime, the spacetime distance between two points is the square root of x^2+y^2+z^2-t^2 (x,y,z in light years, t in years) no matter what your axes are."

So it really isn't distance. Time is not a physical dimension. Time is concept.

No - it IS a distance. Time IS a physical dimension. Its just that the 4-dimensional space in which things exist (spacetime) is not Euclidean. The geometry of things on the surface of a sphere is not Euclidean: the sum of the angles of a triangle on the surface of a sphere do not add up to 180 degrees. The distances in spacetime are not all positive real numbers. So what?

CosmicVoyager said:
Also, if time were a fourth dimension that the universe was in then there are two possibilities, both of in which the above explanation does not work:

Possibility A - Everything in the universe is moving through time. The past and the future are empty. Objects could not be at a different place in time than other objects because they would disappear from the slice of time that the rest of the universe is in.

There is no unique "slice of time" that the universe is in. This is the whole point - the world is four dimensional, objects are four dimensional, and different people make different slices. Your slice is yours, mine is mine. I make a "slice of time" and the universe looks a particular way. You make a different slice, it looks different. Its the same four-dimensional universe, but different slices. Some things that I call "now", you might call "later". A ruler is a four dimensional object. How long is it? One person takes a slice of the 4-D ruler and gets an answer. Another person takes a different slice, gets a different answer. It makes no sense to ask "how long is the ruler?". You have to ask "by whose slice?". This is what the Lorentz contraction is all about.

CosmicVoyager said:
Possibility B - Objects are four dimensional and extend backward in time. They are *extremely*, if not infinitely, long and connect to each other in the past. If this were the case then we should experience all of time at the same time and not just one slice of it, since we are four dimensional objects that are everywhere in time.

But our consciousness does not experience things that way. Our consciousness experiences successive slices of the 4-D universe. If you ask why, then that is a real problem, I don't think anyone knows the answer to that. In that sense, relativity is using equations that tell us what we experience without knowing why. But its not just a bunch of equations, or, if they are, its amazing that they describe a four dimensional space in every bit of detail as the equations we use for our 3-dimensional space, geometry, physics, topology, everything. Searching for a true paradox in the geometry of spacetime is like searching for a paradox in Euclidean geometry. Very, very difficult. All paradoxes boil down to not understanding the geometry of spacetime. All contradictions are indeed apparent, as long as they are based on measurements.
 
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  • #21
"it IS a distance. Time IS a physical dimension. Its just that the 4-dimensional space in which things exist (spacetime) is not Euclidean."

Okay. I'm glad you made that very clear, so there is no ambiguity on that point. It is very important.

"There is no unique "slice of time" that the universe is in. This is the whole point - the world is four dimensional, objects are four dimensional, and different people make different slices. Your slice is yours, mine is mine. I make a "slice of time" and the universe looks a particular way. You make a different slice, it looks different. Its the same four-dimensional universe, but different slices. Some things that I call "now", you might call "later". A ruler is a four dimensional object. How long is it? One person takes a slice of the 4-D ruler and gets an answer. Another person takes a different slice, gets a different answer. It makes no sense to ask "how long is the ruler?". You have to ask "by whose slice?". This is what the Lorentz contraction is all about."

Okay, I'm trying to visualize how all the slices fit together, how they are connected. When one drags a one dimensional line at a right angle perpendicular to itself repeating it over and over, a two dimensional plane is created. And when one drags a plane at a right angle perpendicular to itself, a three dimensional cube is created. When you refer to the fourth dimension, you mean dragging the cube at a right angle perpendicular to itself and getting many cubes with each point in a cube connected to the points in the same place in the previous an next cubes? An entire hypercube can be represented in 3D with a line of cubes and realizing which points are connected. When you say every particle has its own slice, you mean one of those cubes? I can't figure out how to account for observed phenomena with a line of cubes of space where each one is only touching two others just as a each 2D plane in a 3D cube are touching two others. It seems like it would require more dimensions (and I still don't see how to do it LOL) Is it possible to illustrate the same effects with a 2D plane as space and the 3D cube it is in as time?
 
  • #22
CosmicVoyager said:
As I said above,
"If I were to measure out the distances between my mirrors when I am stationary to you, and I and all of the mirrors were to accelerate together, then they should still be arranged in a circle because as the mirrors narrow, the space between them increases since they are not connected."

To which you replied,
"You are correct when you say if the mirrors accelerate together, you mean that you put individual rockets on each mirror and accelerate each of them with no rigid connectors between them but if you mean they are fastened to some kind of structure and you have only one rocket that accelerates the entire structure together, then the mirrors will move closer together."

If I measured them out into a circle, then accelerated and they remained in a circle then they are not in the ellipse needed to make the light appear to travel at the same speed for me as it does for you.
You haven't made it clear but I think you are agreeing that the mirrors are attached to a rigid structure and so are you and when you accelerate, you have only one rocket and you, the rigid structure, the mirrors and the rocket all accelerate together (but not so fast that everything gets destroyed by the g-force). This will allow the rigid frame and the mirrors to take on the elliptical shape (when viewed from the original frame prior to acceleration). But note that you also will take on an elliptical shape and your ruler that you use after acceleration will change its length depending on its orientation so that when you are measuring the vertical distance between the top and bottom mirrors, you will get the same reading as when you measure the horizontal distance between the left and right mirrors. Because everything that has accelerated with you is experiencing length contraction along the direction of acceleration (and of motion with respect to your starting condition), then you cannot tell that any length contraction is going on with you.
CosmicVoyager said:
Anyway, Janus replied saying,
"Length contraction is not something that "physically" acts on objects. It means that reference frames in motion with respect to each other measure the length differently. In other words, if there are two points in space that are 1 meter apart according to you, for someone traveling parallel to the line joining them, these two points will be closer together, regardless of the fact that there is no physical connection between those points or even if there is any physical objects at those point.

So in your above examples, the distances between the discreet objects also length contract."


To which I replied,
"Okay, this is what I was afraid of. It seems to me this "length contraction" idea is just a convenient mathematical correction to compensate for something we have no explanation for, made up so that things will work out in calculations so that it can be predicted how things will *appear* in different circumstances. It is not really happening. Rulers are not contracting. And space is certainly not expanding and contracting based on how fast an object is moving. So it is extremely misleading to say objects flatten the faster they go. The correct answer for how it is that the speed of light can be measured to be the same regardless of one's speed is "No one knows. We only know how to calculate what the results of measurements will be."
I believe Janus was trying to reassure you that your lengths don't contract just because someone else accelerates or just because two other observers watching you are traveling at different speeds.

You are correct that Special Relativity does not explain how things contract or times dilate because it is merely a mathematical theory. But that doesn't mean there aren't other theories that explain the reality of length contraction or time dilation. The purpose of Special Relativity is to integrate measurements that two observers in relative motion make or between the states before and after a single observer accelerates, without regard to explaining any mechanism.

You have to remember that prior to Einstein's paper in 1905 describing Special Relativity, virtually all scientists believed in a universal absolute ether rest condition in which, and only in which, the speed of light was a constant in all directions and in which all dimensions and time intervals were stable and absolute. This is like the green man in my animation and his perfect circle of mirrors. But they assumed that we, on the surface of earth, were traveling through this stationary ether at some unknown speed and in some unknown direction, but our lengths must be contracting and our clocks must be ticking slower than normal in order to account for how we would always measure the speed of light to be exactly the same value as we would if we were stationary in the ether. We are like the red man in my animation. The theory these early scientists developed accounted for how clocks would tick more slowly and lengths would be contracted in the direction of motion through the ether. And they were constantly trying to figure out how to measure or detect this inevitable motion through the ether, without success.

What Einstein did was say that as long as you are not accelerating, you can assume that you are stationary in the ether rest condition and there will be no way to detect that you aren't. So this relieved the scientists of any compulsion to measure or detect any motion through the ether and allowed them to proceed with physical theories without concern about identifying any ether.

But this raises a question: suppose there really is an ether and suppose we are traveling through it at a very high speed in some direction, just by being stationary on the surface of the earth. We won't be able to tell, but we would certainly understand in principle that we would be experiencing length contraction and time dilation. Now suppose that we get in our rocket and take off at a very high speed into space and it just so happens by pure chance that we are traveling into the either such that our speed through the ether was now less than it was before, in fact, let's pretend that we are now stationary in the ether. What would we say about length contraction and time dilation? Well, if we assumed that we were at rest in the ether when still back on earth, we would have to now say that our lengths were contracted and our times dilated. But, since we are imagining that we really were traveling through the ether before and now we are at rest in the ether then our lengths would be longer and our clocks would tick at a faster rate. This explains why we can never say in an absolute sense that when you see something traveling at a high speed that it is experiencing length contraction and time dilation as it may be the other way around for all we know.

Again, please, if any of this is confusing or doesn't make sense or has apparent contradictions, then just ask.
 
  • #23
ghwellsjr said:
You haven't made it clear but I think you are agreeing that the mirrors are attached to a rigid structure and so are you and when you accelerate, you have only one rocket and you, the rigid structure, the mirrors and the rocket all accelerate together (but not so fast that everything gets destroyed by the g-force)."

Ack! No! :-)

"You are correct when you say if the mirrors accelerate together, you mean that you put individual rockets on each mirror and accelerate each of them with no rigid connectors between them"

Yes, if I measured them out into a circle, then accelerated *unconnected* and they remained in a circle then they are not in the ellipse needed to make the light appear to travel at the same speed for me as it does for you. That is the problem the length contraction idea. From my point of view my ruler did not change when I accelerated, so I should measure the speed of light to be c, but I would not because the length contraction needed to make the circle an eclipse does not happen because the mirrors are not connected. From my point of view, light would not be measured to be c is as supposed to be the case.

Also, I think we should be able to detect the delay between the particles that make up an object narrowing and all the particles moving toward the center to fill the space. The longer the object is, the longer it takes the edges to finish moving in. I know we can measure time dilation in a moving clock, and I know we can measure time dilation due to gravity just one foot closer to the earth!
http://news.nationalgeographic.com/news/2010/09/100922-science-space-time-einstein-relativity-aging-gravity-earth/
 
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  • #24
"You are correct that Special Relativity does not explain how things contract or times dilate because it is merely a mathematical theory."

That is what I suspect!"But that doesn't mean there aren't other theories that explain the reality of length contraction or time dilation."

That is what I want to know!"The purpose of Special Relativity is to integrate measurements that two observers in relative motion make or between the states before and after a single observer accelerates, without regard to explaining any mechanism."

That is what I was saying.
 
  • #25
CosmicVoyager said:
Okay, I'm trying to visualize how all the slices fit together, how they are connected. When one drags a one dimensional line at a right angle perpendicular to itself repeating it over and over, a two dimensional plane is created. And when one drags a plane at a right angle perpendicular to itself, a three dimensional cube is created. When you refer to the fourth dimension, you mean dragging the cube at a right angle perpendicular to itself and getting many cubes with each point in a cube connected to the points in the same place in the previous an next cubes? An entire hypercube can be represented in 3D with a line of cubes and realizing which points are connected. When you say every particle has its own slice, you mean one of those cubes? I can't figure out how to account for observed phenomena with a line of cubes of space where each one is only touching two others just as a each 2D plane in a 3D cube are touching two others. It seems like it would require more dimensions (and I still don't see how to do it LOL) Is it possible to illustrate the same effects with a 2D plane as space and the 3D cube it is in as time?

Yes, except that you would not say the 3D cube is time, you would say that the direction you are dragging the 2D square is the time direction and the 3D cube is a cube in spacetime.

Now somebody else tilts the piece of paper and drags it in a perpendicular direction. They create a different cube in spacetime. The direction they are dragging it in is their time direction. You are both dragging your square pieces of paper through the same spacetime, but your cube is tilted with respect to their cube.

What I am saying is, when you make the first cube in spacetime, the infinite plane containing that sheet of paper is your "time slice" through spacetime. When somebody else tilts the paper, the plane of that piece of paper is their "time slice" through spacetime. Different people experience different slices. The direction you move your paper is perpendicular to your paper. That is your "time direction". The direction the other person moves their paper is perpendicular to their paper. That is their "time direction".

Take a pencil and make a point in the middle of your paper. That represents you. Your paper always stays motionless with respect to you as you move through time and your point draws out a line. That line is called your "world line". The other person makes a point on their paper, that's them. Their paper always stays motionless with respect to them, and the line that their point traces out as they move their paper is their "world line". But what happens when you move the plane of your paper through the other person's world line? It moves on your piece of paper! The other person is moving with respect to you! If they look at your world line on their piece of paper, your world line moves on their piece of paper, so they say you are moving with respect to them. Thats why we say that if two people are moving with respect to each other, their "time slices" and "world lines" are tilted with respect to each other.
 
  • #26
I am struggling to understand what you are saying. Further questions depend on the answer to this question: I meant for the 2D plane to represent our 3D universe. Did you realize that? Is that how you are using it? I ask because you talk about me moving the piece of paper in one direction or someone else moving the peace of paper in another direction. You seem be saying I am outside the universe moving it. I wanted to know if you could show how objects move in the 2D plane for space and through 3D for time.

"the infinite plane containing that sheet of paper is your "time slice" through spacetime. When somebody else tilts the paper, the plane of that piece of paper is their "time slice" through spacetime."

It sounds like you are saying we are holding the universe or that we are in different universes.

I need an illustration that shows two objects or people moving at different speeds measuring the speed of light from the same source. An illustration that reconciles the apparent contradiction that they measure it to be the same speed. Like this animation tries to do What I mean by "like this animation" is that it shows both people in the same universe, and how it might be that light appears the same speed to both.

"Take a pencil and make a point in the middle of your paper. That represents you. Your paper always stays motionless with respect to you as you move through time and your point draws out a line. That line is called your "world line". The other person makes a point on their paper, that's them."

They need to be on the same paper! lol Or at least the same cube. The paper is the space of the universe. If they are on separate paper it is like they are in different universes and there is no reconciliation of their views. I'm trying to see how their apparently opposing views can exist in the same universe, in the same space time continuum. You said there are 3 dimensions of space and a 4th of time. The 2D plane is supposed to represent our 3D space. If you are moving the paper in any way other than dragging it exactly perpendicular, more than 4 dimensions are needed.
 
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  • #27
CosmicVoyager said:
I meant for the 2D plane to represent our 3D universe. Did you realize that? Is that how you are using it? I ask because you talk about me moving the piece of paper in one direction or someone else moving the peace of paper in another direction. You seem be saying I am outside the universe moving it. I wanted to know if you could show how objects move in the 2D plane for space and through 3D for time.

Yes, that's exactly how I meant it. The whole plane in which your 2D piece of paper sits represents the 3D universe as you see it now, and the 3D space that it is moving through represents spacetime. The direction that your piece of paper is moving is your time direction. Your paper, as it moves perpendicular to itself represents the universe, as you see it, moving through spacetime.

CosmicVoyager said:
"the infinite plane containing that sheet of paper is your "time slice" through spacetime. When somebody else tilts the paper, the plane of that piece of paper is their "time slice" through spacetime."

It sounds like you are saying we are holding the universe or that we are in different universes.

You are both in the 3D spacetime, spacetime never changes. Your 2D piece of paper is a slice through the 3D spacetime. Everything in your paper happens "now" to you, as it moves through spacetime. Another person with another piece of paper is moving through spacetime at a different angle. Their piece of paper makes a different slice through spacetime. Everything in their piece of paper happens "now" to them. Yes, you experience spacetime differently from them. If two firecrackers, go off at the same time, according to you, the other person will say no, they did not go off at the same time, one went off before the other.

CosmicVoyager said:
I need an illustration that shows two objects or people moving at different speeds measuring the speed of light from the same source. An illustration that reconciles the apparent contradiction that they measure it to be the same speed. Like this animation tries to do What I mean by "like this animation" is that it shows both people in the same universe, and how it might be that light appears the same speed to both.


Don't worry about the speed of light right now. That comes later. Right now you have to understand about how different people experience spacetime and why, and I think you are on the right track, but not there yet.

CosmicVoyager said:
"Take a pencil and make a point in the middle of your paper. That represents you. Your paper always stays motionless with respect to you as you move through time and your point draws out a line. That line is called your "world line". The other person makes a point on their paper, that's them."

They need to be on the same paper! lol Or at least the same cube. The paper is the space of the universe. If they are on separate paper it is like they are in different universes and there is no reconciliation of their views.

There is no unique "space of the universe". They do not have to be on the same paper! This is what Einstein discovered! There will be no reconciliation of their views only if they fail to understand what is happening. Once they understand that spacetime is where everything happens, and they are only taking slices through spacetime, they will be able to reconcile everything.

If two people are moving with respect to each other, the slices through spacetime which they call "the universe as I see it now" are different. Spacetime is what it is, so yes, they can disagree on whether two firecrackers went off at the same time, or how far apart they were when they went off, but they will always agree that two firecrackers went off, because two firecrackers went off in spacetime, no matter what angle you look at it from.

CosmicVoyager said:
I'm trying to see how their apparently opposing views can exist in the same universe, in the same space time continuum. You said there are 3 dimensions of space and a 4th of time. The 2D plane is supposed to represent our 3D space. If you are moving the paper in any way other than dragging it exactly perpendicular, more than 4 dimensions are needed.

Your paper is moving perpendicular to its plane through spacetime. Someone else's paper is moving perpendicular to the plane of their paper through spacetime. You say "I'm trying to see how their apparently opposing views can exist in the same universe". The answer is "by understanding that they are experiencing slices through a 3-D spacetime"

You have two eyes. They give you slightly different 2-D views of the same scene. How can these two apparently opposing views be reconciled? By realizing that they are viewing a 3-D scene from slightly different angles. Thats how they are reconciled.

You have to get rid of the idea that what you call "the universe as it is now" is the same as what a person moving with respect to you calls "the universe as it is now". The fact that this causes disagreements about space and time is to be expected. But just like the disagreements between your two eyes, once you understand that another dimension is involved, all the disagreements are explained and everything is fine.
 
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  • #28
"You have to get rid of the idea that what you call "the universe as it is now" is the same as what a person moving with respect to you calls "the universe as it is now"."

OH MY GOD! AHHHH! This conversation has been a waste of time then :-/ *Hangs head is despondence*"The direction that your piece of paper is moving is your time direction. Your paper, as it moves perpendicular to itself represents the universe, as you see it, moving through spacetime."

I already know that! I already know what special relativity says.

So you have not been trying to answer what I want to know. I already know that everyone at different velocities view things differently. All you have been doing is trying to give separate illustrations of their points of view. Every time I have responded to something you posted, it is because you were going in the direction of not explaining things in *one* illustration of the spacetime continuum."Your 2D piece of paper is a slice through the 3D spacetime. Everything in your paper happens "now" to you, as it moves through spacetime. Another person with another piece of paper is moving through spacetime at a different angle."

That is just telling what I already know. That there are two perspectives. If you can't put them together, then there is a contradiction. The universe is in one state or another. Otherwise, there would have to be different universe for every particle."There is no unique "space of the universe". This is what Einstein discovered!"

I already know that point of view! He did not discover that that there *is no* space time universe. He created a mathematical system to predict how things will *appear* to be under different circumstances. It is abstract. We can't say that there is no space time of the universe."They do not have to be on the same paper!"

I disagree. To make sense they do. For everything to be in the same universe they do. There is only one universe. If you read my original post, the point of it is to point out that according to what you are saying, the photon in question would have to be in two different places at the same time, or that space would have to different lengths at the same time. That is why someone posted an animation showing that light was not really traveling at c, but appeared to due to time dilation and length contraction because of speed. I thought you were going to be able to produce an explanation like that with everything that is happening to both observers *in the same* single illustration of spacetime.

Saying "there is no unique "space of the universe" is like metaphysics. That is saying there is no objective reality. That every particle sees different contradictory states of the universe. There must be no contradictions. There has to be way to show why the speed of light *appears* to move the same speed relative to any observer. Otherwise there would have to be a different universe for every particle.In one place you seemed to be saying what I am saying:
"You are both in the 3D spacetime, spacetime never changes. Your 2D piece of paper is a slice through the 3D spacetime."

So show that single spacetime. If mine is a slice and someone else's is a slice, then combine the slices into one picture.
 
  • #29
CosmicVoyager said:
So show that single spacetime. If mine is a slice and someone else's is a slice, then combine the slices into one picture.
(In this reduced dimension model)
You just stack all your 2D space slices together and you get 3D spacetime.
I just stack all my 2D space slices together and I get 3D spacetime.
We both get the same single 3D spacetime even though we disagree on what the 2D space slices are.

(Add one to all the dimensions above for the real answer, of course.)
 
  • #30
DrGreg said:
(In this reduced dimension model)
You just stack all your 2D space slices together and you get 3D spacetime.
I just stack all my 2D space slices together and I get 3D spacetime.
We both get the same single 3D spacetime even though we disagree on what the 2D space slices are.

(Add one to all the dimensions above for the real answer, of course.)

You say "we both get the same single 3D spacetime". So the illustrations are identical? There is one arrangement of objects?

If not, another thread is discussing whether or not the speed of light is just measured to be constant relative to all observers.
https://www.physicsforums.com/showthread.php?t=482318

In this thread I asking for a single arrangement of objects in spacetime and any relevant phenomena that shows why light *appears* to be the same speed relative to any observer.
 
  • #31
CosmicVoyager said:
ghwellsjr said:
You haven't made it clear but I think you are agreeing that the mirrors are attached to a rigid structure and so are you and when you accelerate, you have only one rocket and you, the rigid structure, the mirrors and the rocket all accelerate together (but not so fast that everything gets destroyed by the g-force).
Ack! No! :-)
ghwellsjr said:
You are correct when you say if the mirrors accelerate together, you mean that you put individual rockets on each mirror and accelerate each of them with no rigid connectors between them.

Yes, if I measured them out into a circle, then accelerated *unconnected* and they remained in a circle then they are not in the ellipse needed to make the light appear to travel at the same speed for me as it does for you. That is the problem the length contraction idea. From my point of view my ruler did not change when I accelerated, so I should measure the speed of light to be c, but I would not because the length contraction needed to make the circle an eclipse does not happen because the mirrors are not connected. From my point of view, light would not be measured to be c is as supposed to be the case.
But, if you measured the mirrors out into a circle and then accelerated them unconnected, then after you were done accelerating and you measured the shape of the mirrors with the same ruler you used before, you would see that they were no longer in a circle. Instead, it would look to you like a stretched out ellipse. Your ruler is a rigid object so it will contract along with you and everything else that is rigid, that's why you cannot tell that it has contracted.
CosmicVoyager said:
Also, I think we should be able to detect the delay between the particles that make up an object narrowing and all the particles moving toward the center to fill the space. The longer the object is, the longer it takes the edges to finish moving in. I know we can measure time dilation in a moving clock, and I know we can measure time dilation due to gravity just one foot closer to the earth!
http://news.nationalgeographic.com/news/2010/09/100922-science-space-time-einstein-relativity-aging-gravity-earth/
You say "we should be able to detect the delay between particles"...did you mean the gap between the particles? The problem is that anything we use to measure distances will also be subjected to exactly the same length contraction which makes it impossible to directly tell that it is happening. But the fact that light clocks or any other kind of clock experiences time dilation as you pointed out, and the fact that the orientation of the clock does not effect the time dilation, indirectly proves that it must be happening.
 
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  • #32
"But, if you measured the mirrors out into a circle and then accelerated them unconnected, then after you were done accelerating and you measured the shape of the mirrors with the same ruler you used before, you would see that they were no longer in a circle. Your ruler is a rigid object so it will contract along with you and everything else that is rigid, that's why you cannot tell that it has contracted."

Okay. So my ruler will shrink, but not from my point of view. Hmm...so if my ruler narrows but the circle does not, then to me the circle appears to get wider. I am having trouble picturing what the effect of that would be, but according to the animation what is needed is for the circle to be narrower from the other person's, your, point of view, which it is not if I measured it out while at rest relative to you."You say "we should be able to detect the delay between particles"...did you mean the gap between the particles?"

I mean that the particles that make up the object get narrower. This increases the space between them. The object narrows as the forces binding the particles together pull the particles together to fill the space."The problem is that anything we use to measure distances will also be subjected to exactly the same length contraction which makes it impossible to directly tell that it is happening."

There would be a delay as the object as a whole finishes contracting, and a delay in the effects of that contraction. The further the edges, the longer the delay. So briefly, at the edges, one would not measure the speed of light to be c."But the fact that light clocks or any other kind of clock experiences time dilation as you pointed out, and the fact that the orientation of the clock does not effect the time dilation, indirectly proves that it must be happening."

I have researched and everything I read says length contraction has not been proven experimentally. There are experiments planned such as the Space Interferometry Mission.

I don't know what you mean about the clock orientation. Why would you expect the orientation of the clock to matter if there is no length contraction?
 
  • #33
CosmicVoyager said:
Every time I have responded to something you posted, it is because you were going in the direction of not explaining things in *one* illustration of the spacetime continuum.

But it is *one* illustration of the spacetime continuum. That 3D spacetime continuum, as I have described it contains two world lines at angles to each other. Yours and the other persons. That's all.

Let me ask - what do you mean when you say "universe"? There is the spatial universe that you see now. Then there is spacetime, which contains the universe, past, present and future. What do you mean when you say "universe"?

CosmicVoyager said:
"Your 2D piece of paper is a slice through the 3D spacetime. Everything in your paper happens "now" to you, as it moves through spacetime. Another person with another piece of paper is moving through spacetime at a different angle."

That is just telling what I already know. That there are two perspectives. If you can't put them together, then there is a contradiction. The universe is in one state or another. Otherwise, there would have to be different universe for every particle.

Again, what do you mean by "universe"?. If you mean spacetime, then yes, it is in only one state. There is only one spacetime. If you mean the spatial universe that you experience "now", then there are an infinite number of separate universes, all coherently tied together by the fact that they are slices through the unvarying spacetime.

All physics happens in spacetime. What we call a particle is a curve in spacetime. If the particle decays into two other particles, then that curve separates into two distinct curves in spacetime. It doesn't matter how you slice it, those curves are the single picture of what is going on. They do not depend on you or somebody else to observe them to decide which way they are going to twist and turn. As an observer, you take a slice thru spacetime, and say "that is what I experience". Another person takes another slice, and they say "that is what I experience". The curves don't know and don't care who, if anybody, is observing them.
CosmicVoyager said:
He created a mathematical system to predict how things will *appear* to be under different circumstances. It is abstract.

When I say that the distance between two points is the square root of x^2+y^2+z^2, is that an abstract mathematical system? Or is it a description of the geometry of space?

CosmicVoyager said:
"They do not have to be on the same paper!"

I disagree. To make sense they do. For everything to be in the same universe they do. There is only one universe. If you read my original post, the point of it is to point out that according to what you are saying, the photon in question would have to be in two different places at the same time, or that space would have to different lengths at the same time.

But this is the very problem I am trying to explain. Try this - space does not have a length. 3D space does not have a length. If you put two dots on a wall in 3D space, and take a picture of them, then you can talk about the distance between the dots on the picture. If you take a picture from a different angle, you can talk about the length between them on the second picture. Finally, you can go out and measure the distance between the dots on the wall. When you say "or that space would have to different lengths at the same time" its like saying your camera must take two different pictures at the same angle. The distance between the dots on the wall is independent of which angle you look at them from. In the same way, the spacetime distance between two events is the same for every observer, no matter how they are moving.

Read your statement again - "or that space would have to different lengths at the same time". It is proof that you do not yet understand relativity. There is no such thing as "the same time" for the two different observers. There is no such thing as "the same angle" for the two different pictures taken at different angles.

CosmicVoyager said:
Saying "there is no unique "space of the universe" is like metaphysics. That is saying there is no objective reality. That every particle sees different contradictory states of the universe. There must be no contradictions. There has to be way to show why the speed of light *appears* to move the same speed relative to any observer. Otherwise there would have to be a different universe for every particle.

Again, what do you call "the universe"?. Here you seem to be calling the universe as the space of the universe as you see it now. There IS objective reality in the theory of relativity. That objective reality is spacetime. Every particle sees different, BUT NOT CONTRADICTORY, spatial universes. Just because they give measurements of space and time intervals which do not agree, does not mean that they are in contradiction, any more than the two photographs are in contradiction because they give two different pictures when taken at two different angles.
CosmicVoyager said:
In one place you seemed to be saying what I am saying:
"You are both in the 3D spacetime, spacetime never changes. Your 2D piece of paper is a slice through the 3D spacetime."

So show that single spacetime. If mine is a slice and someone else's is a slice, then combine the slices into one picture.

The single spacetime, for you and the other observer consists of two lines in spacetime that are not parallel. That is the one picture you are looking for. The two lines and the spacetime in which they exist are the one picture.
 
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  • #34
( I have replaced plane and cube with 2D grid and 3D grid. That is more accurate since spacetime might be bent))

When I say "universe" I mean all existing matter, energy, and space (and time if it is physical and not abstract.). This would be a line of 3D grids, each 3d grid being a location on the time axis. Or analogously, a series of 2D grids.

If the universe appears to be different, if things appear to be in different location, then it must be just that, *appearance*."unvarying spacetime."

When you say "unvarying spacetime", do you mean there is a 4-dimensional universe of matter, energy, and space (and the 4th dimension, time) that can be represented with single illustration? (If we could draw in in 4D. Instead we have to repeat a 3D space over and over with a line of 3D grids, or use a 3D analogy.) Because you keep giving multiple illustrations. Can you make a single illustration of two observers and a light source in 4D or a 3D analog? If not, then you are not saying there is unvarying spacetime.

If there is a single unvarying spacetime, then it should be possible able to show what is going on with two observers and a light source a single series of 2D grids, that is, with a single 3D grid.
 
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  • #35
CosmicVoyager said:
"But, if you measured the mirrors out into a circle and then accelerated them unconnected, then after you were done accelerating and you measured the shape of the mirrors with the same ruler you used before, you would see that they were no longer in a circle. Your ruler is a rigid object so it will contract along with you and everything else that is rigid, that's why you cannot tell that it has contracted."

Okay. So my ruler will shrink, but not from my point of view. Hmm...so if my ruler narrows but the circle does not, then to me the circle appears to get wider. I am having trouble picturing what the effect of that would be, but according to the animation what is needed is for the circle to be narrower from the other person's, your, point of view, which it is not if I measured it out while at rest relative to you.
The effect of the mirrors accelerating with their own rockets and thus ending up farther apart than they should be (along the direction of acceleration) to form the correct ellipse is that you would no longer see the light returning back to you from all the mirrors at the same time. The reflections from the top and bottom mirrors would arrive first and the reflections from the mirrors along the direction of acceleration would arrive last, with the other mirrors in between. You would not conclude that you were in the center of the expanding sphere of light. Until, of course, you checked the dimensions of your setup and discovered that the mirrors were no longer arranged in a perfect circle.
CosmicVoyager said:
"You say "we should be able to detect the delay between particles"...did you mean the gap between the particles?"

I mean that the particles that make up the object get narrower. This increases the space between them. The object narrows as the forces binding the particles together pull the particles together to fill the space.
I still don't know why you use the word "delay". Delay has to do with time or speed and I don't see anything in your comments that have to do with either one of those. I'm also not sure if you are expressing a problem that you want someone to help resolve for you or if you are just making an observation.
CosmicVoyager said:
"The problem is that anything we use to measure distances will also be subjected to exactly the same length contraction which makes it impossible to directly tell that it is happening."

There would be a delay as the object as a whole finishes contracting, and a delay in the effects of that contraction. The further the edges, the longer the delay. So briefly, at the edges, one would not measure the speed of light to be c.
If you are suggesting that during the time when you are starting and stopping an acceleration that the measurement of the speed of light will be compromised, then yes, that is true.
CosmicVoyager said:
"But the fact that light clocks or any other kind of clock experiences time dilation as you pointed out, and the fact that the orientation of the clock does not effect the time dilation, indirectly proves that it must be happening."

I have researched and everything I read says length contraction has not been proven experimentally. There are experiments planned such as the Space Interferometry Mission.

I don't know what you mean about the clock orientation. Why would you expect the orientation of the clock to matter if there is no length contraction?
A light clock formed with a circle of mirrors would behave the same way no matter its orientation because it is symmetrical. But suppose you had a conventional light clock with just two mirrors and a burst of light bouncing back and forth between them, marking off equal time intervals. Now don't you agree that if the mirrors are oriented so that the burst of light is traveling along the direction of motion and then you rotated it 90 degrees, that it will keep a different time if there is no length contraction?

What would constitute a proof of length contraction for you? If someone were to construct and arrangement of mirrors like I show in the animation and no matter how they accelerated, they always see the light from all mirrors arriving simultaneously, would that be proof of length contraction? If not, what would an experiment be like that you would accept?
 
<h2>What is relativity?</h2><p>Relativity is a theory developed by Albert Einstein that explains the relationship between space and time. It states that the laws of physics are the same for all observers, regardless of their relative motion.</p><h2>What is the scenario used to understand relativity?</h2><p>The most commonly used scenario to understand relativity is the "Twin Paradox". This scenario involves two twins, one stays on Earth while the other travels in a high-speed rocket. When the traveling twin returns, they have aged less than the twin who stayed on Earth, demonstrating the effects of time dilation.</p><h2>How does relativity affect our daily lives?</h2><p>Relativity has many practical applications in our daily lives, such as in GPS technology. The satellites in GPS systems have to take into account the effects of relativity in order to accurately calculate and transmit location data.</p><h2>What is the difference between special and general relativity?</h2><p>Special relativity deals with the relationship between space and time in the absence of gravity, while general relativity includes the effects of gravity. Special relativity is used for objects moving at constant speeds, while general relativity is used for objects in accelerated motion or in the presence of massive objects.</p><h2>What evidence supports the theory of relativity?</h2><p>There is a significant amount of evidence that supports the theory of relativity, including the observed bending of light around massive objects, the time dilation effects seen in high-speed particles, and the accurate predictions made by the theory in various experiments and observations.</p>

What is relativity?

Relativity is a theory developed by Albert Einstein that explains the relationship between space and time. It states that the laws of physics are the same for all observers, regardless of their relative motion.

What is the scenario used to understand relativity?

The most commonly used scenario to understand relativity is the "Twin Paradox". This scenario involves two twins, one stays on Earth while the other travels in a high-speed rocket. When the traveling twin returns, they have aged less than the twin who stayed on Earth, demonstrating the effects of time dilation.

How does relativity affect our daily lives?

Relativity has many practical applications in our daily lives, such as in GPS technology. The satellites in GPS systems have to take into account the effects of relativity in order to accurately calculate and transmit location data.

What is the difference between special and general relativity?

Special relativity deals with the relationship between space and time in the absence of gravity, while general relativity includes the effects of gravity. Special relativity is used for objects moving at constant speeds, while general relativity is used for objects in accelerated motion or in the presence of massive objects.

What evidence supports the theory of relativity?

There is a significant amount of evidence that supports the theory of relativity, including the observed bending of light around massive objects, the time dilation effects seen in high-speed particles, and the accurate predictions made by the theory in various experiments and observations.

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