Do we live in 3 or 4 dimensions?

[Stricklandjr]

pleese don't critical on my little knowledge of this. a few of us have bull sessions sometimes and my cousin points front side up and says we live in 3 dimencions but the whole universe is 4 dimencions. this other guy always says my cousin is full of bull and einstine just used them for calculations. who is right?

also I'm new and read the rules for this forums. what did greg mean by you can't bring up ether theory?

 

[phinds]

spacetime is a 4 vector, so while we DO live in 3 SPATIAL dimensions, we also do live in 4 dimensions so they are both right. If one of them is saying we live in 4 dimension of space, then he misunderstands Einstein.

"Ether theory" is a theory you can find on Google. It was discredited something like 100 years ago and is not discussed on this forum.

 

[Stricklandjr]

spacetime is a 4 vector, so while we DO live in 3 SPATIAL dimensions, we also do live in 4 dimensions so they are both right. If one of them is saying we live in 4 dimension of space, then his misunderstands Einstein.

"Ether theory" is a theory you can find on Google. It was discredited something like 100 years ago and is not discussed on this forum.

sorry I don't understand when you first say we also do live in 4 dimensions and then if one of them is saying we live in 4 dimension of space he misunderstands Einstein.

 

[tensor33]

sorry I don't understand when you first say we also do live in 4 dimensions and then if one of them is saying we live in 4 dimension of space he misunderstands Einstein.

What phinds is saying is that we live in a 4 dimensional world where 3 dimensions are spatial, and the fourth is time. It is incorrect to say that we live in 4 spatial dimensions.

 

[Stricklandjr]

What phinds is saying is that we live in a 4 dimensional world where 3 dimensions are spatial, and the fourth is time. It is incorrect to say that we live in 4 spatial dimensions.

ok. thank you. I'm looking at some other threads and there is one by a guitar name about us moving through the 4 dimensional universe as fast as light. Does that mean that the universe is 4 dimensions (space and time) and we are just 3 dimensional moving through the 4 dimensions of the universe? So things like rocks and cars and people are three dimensions and the universe is 4 dimensions?

 

[HallsofIvy]

Physics deals with "events"- things that happen at a given point in space at a given time. In any coordinate system we need 3 numbers to specify the point and one to specify the time. That's what "four dimensional" means.

 

[PeterDonis]

I'm looking at some other threads and there is one by a guitar name about us moving through the 4 dimensional universe as fast as light.

We get a lot of threads here about that. It's not wrong, exactly, but it can easily lead to misconceptions. The basic physical fact underlying the statement is that every object (more precisely, every object with nonzero rest mass) has a 4-velocity vector whose length is the speed of light.

Does that mean that the universe is 4 dimensions (space and time) and we are just 3 dimensional moving through the 4 dimensions of the universe?

On the view I just described, where an "object" has a single 4-velocity vector, the object is idealized as point-like, so its path through 4-dimensional spacetime is a 1-dimensional line, called its "worldline". A real object, which is extended in space, would be modeled as a whole family of worldlines that stay together; this is sometimes called a "world-tube". But if individual parts of the extended object are moving with respect to each other, they will not all have the same 4-velocity, so you can't assign a single 4-velocity vector to the entire object. (Often you can assign a sort of "average" 4-velocity to the object because all of its parts are moving really slowly with respect to each other, compared to the speed of light. But that's an approximation.)

However, it's important to note that in all these models, the "object" (whether its an idealized point-like object or an object extended in space) is best viewed as its worldline or world tube. This is because of the relativity of simultaneity; different observers in different states of motion will "slice" 3-dimensional sections out of an extended object's world tube in different ways. So you can't really view the object as a 3-dimensional thing that moves through time; you have to look at its entire 4-dimensional world tube. When your cousin said that we live in 3 dimensions, he apparently wasn't taking that into account.

 

[Naty1]

Check out some descriptions here:

http://en.wikipedia.org/wiki/Spacetime

 

[Stricklandjr]

We get a lot of threads here about that. It's not wrong, exactly, but it can easily lead to misconceptions. The basic physical fact underlying the statement is that every object (more precisely, every object with nonzero rest mass) has a 4-velocity vector whose length is the speed of light.



On the view I just described, where an "object" has a single 4-velocity vector, the object is idealized as point-like, so its path through 4-dimensional spacetime is a 1-dimensional line, called its "worldline". A real object, which is extended in space, would be modeled as a whole family of worldlines that stay together; this is sometimes called a "world-tube". But if individual parts of the extended object are moving with respect to each other, they will not all have the same 4-velocity, so you can't assign a single 4-velocity vector to the entire object. (Often you can assign a sort of "average" 4-velocity to the object because all of its parts are moving really slowly with respect to each other, compared to the speed of light. But that's an approximation.)

However, it's important to note that in all these models, the "object" (whether its an idealized point-like object or an object extended in space) is best viewed as its worldline or world tube. This is because of the relativity of simultaneity; different observers in different states of motion will "slice" 3-dimensional sections out of an extended object's world tube in different ways. So you can't really view the object as a 3-dimensional thing that moves through time; you have to look at its entire 4-dimensional world tube. When your cousin said that we live in 3 dimensions, he apparently wasn't taking that into account.

Boy! You are really getting down to it. This is getting interesting even for a dumb guy like me. I took a course in physics in junior college and at the end of the semester he told us about relativity but never really talked about what you are saying, he did use some equations though. My cousin has had more college courses in physics and we all talk about it sometimes. Then do you mean the the objects you talk about are really 4 dimensional just like space (and time)? Are things really 4 dimensions and we just don't see all of the dimensions?

 

[PeterDonis]

Then do you mean the the objects you talk about are really 4 dimensional just like space (and time)?

Just like *spacetime*, yes. (Neither space nor time by themselves are 4-dimensional; only spacetime is.)

Are things really 4 dimensions and we just don't see all of the dimensions?

What makes you think we don't see all the dimensions? The 4th dimension is time; we "see" the time dimension by observing that objects don't just exist for an instant; they exist for some length of time.

 

[Naty1]

Strickland asks:

So things like rocks and cars and people are three dimensions and the universe is 4 dimensions?

Then do you mean the the objects you talk about are really 4 dimensional just like space (and time)? Are things really 4 dimensions and we just don't see all of the dimensions?

Here are two famous quotes that address your question in a humorous but interesting way:

"Time is what keeps everything from happening at once."

and I think it might have been Richard Feynman who said

"Space is what keeps everything from happening to me.'

I took a course in physics in junior college and at the end of the semester he told us about relativity but never really talked about what you are saying...

When you learned Newtonian physics the implicit assumptions used three dimensions of space, say (x,y,z) and an independent parameter time, t, which ticks along the same steady rate for everyone. And the assumed infinite speed of light allowed things to happen instantaneously...so it took no time for sunlight to get from the sun to us. Everybody measures the same distances and times. All this works pretty well when relative speeds are slow...like orbiting planets.

Einstein figured out that space and time are actually relative and depend on each other. 'Space' [distances] that appear fixed in our everyday slow speed existence can be different for different high speed observers. That is, the speed of light is finite and, crazy as it seems, everybody measures the same speed for light no matter their own local speed. So space and time vary by observer, related to their speeds, while the speed of light is finite and fixed.

In fact it was Einstein's college teacher, Minkowski, who realized that Einstein's early work meant that space and time should be treated equally, that events take place in four-dimensional space-time. Space and time were no longer to be considered separate, independent entities! So the three 'dimensions' of Newton (x,y,z) became four dimensions [spacetime] of relativity: (t,x,y,z).

edit: If I have stated things correctly here, it should all be consistent with what PeterDonis has posted. The inexpensive book FABRIC OF THE COSMOS by Brian Greene describes 'moving through spacetime at the speed of light' and a lot more without any math. I found that book to be fascinating reading when I started reviewing relativity.

 

[Stricklandjr]

Just like *spacetime*, yes. (Neither space nor time by themselves are 4-dimensional; only spacetime is.)

You are blowing me away with these ideas Dr. Donis. My mind is spinning. But I think I am beginning to catch on some.

What makes you think we don't see all the dimensions? The 4th dimension is time; we "see" the time dimension by observing that objects don't just exist for an instant; they exist for some length of time.

Now I think I am beginning to get it. I really liked taking computer drawing in jr college. With this program called I-Deas you could sketch a 2 dimensional surface and then just extend it into the 3rd dimension for whatever length you choose. So maybe relativity is a little like starting with a 3 dimensional thing and then extending it along the 4th dimension. Along a path you called a world tube? So if I see a rock on the ground I could imagine extending it along its world tube? This is heavy stuff. You are about the smartest physicist here. How could anyone ever figure out that was what is going on?

 

[Stricklandjr]

Strickland asks:





Here are two famous quotes that address your question in a humorous but interesting way:



and I think it might have been Richard Feynman who said





When you learned Newtonian physics the implicit assumptions used three dimensions of space, say (x,y,z) and an independent parameter time, t, which ticks along the same steady rate for everyone. And the assumed infinite speed of light allowed things to happen instantaneously...so it took no time for sunlight to get from the sun to us. Everybody measures the same distances and times. All this works pretty well when relative speeds are slow...like orbiting planets.

Einstein figured out that space and time are actually relative and depend on each other. 'Space' [distances] that appear fixed in our everyday slow speed existence can be different for different high speed observers. That is, the speed of light is finite and, crazy as it seems, everybody measures the same speed for light no matter their own local speed. So space and time vary by observer, related to their speeds, while the speed of light is finite and fixed.

In fact it was Einstein's college teacher, Minkowski, who realized that Einstein's early work meant that space and time should be treated equally, that events take place in four-dimensional space-time. Space and time were no longer to be considered separate, independent entities! So the three 'dimensions' of Newton (x,y,z) became four dimensions [spacetime] of relativity: (t,x,y,z).

edit: If I have stated things correctly here, it should all be consistent with what PeterDonis has posted. The inexpensive book FABRIC OF THE COSMOS by Brian Greene describes 'moving through spacetime at the speed of light' and a lot more without any math. I found that book to be fascinating reading when I started reviewing relativity.

I think this is just what Dr. Donis was saying. But I am going to the book store today and look for that book. And I have to think hard about how the 4 dimensions are not just space but what you and Dr. Donis call spacetime. When I think about the way I did drafting I can picture a rock extending into the 4th dimension but I have to think some more about how that could be something new called spacetime. Is it some kind of combination of space and time that is too hard for us to imagine what it is or do you and Dr. Donis know what it is?

 

[phinds]

I think this is just what Dr. Donis was saying. But I am going to the book store today and look for that book. And I have to think hard about how the 4 dimensions are not just space but what you and Dr. Donis call spacetime. When I think about the way I did drafting I can picture a rock extending into the 4th dimension but I have to think some more about how that could be something new called spacetime. Is it some kind of combination of space and time that is too hard for us to imagine what it is or do you and Dr. Donis know what it is?

Your statement of the question "what is it?" is not helpful. "WHAT" something is is just a name we give it. In this case we give it the name "spacetime". There is no other answer to WHAT it is. Science is about describing the properties of the things we give names to and the properties of spacetime are discussed in general relativity.

A really excellent example of this terminology issue is the confusion that was experienced early in the days of quantum mechanics when people insisted on calling a photon either a "wave" or a "particle" because they were hung up on WHAT it is. In reality, a photon is NEITHER a wave nor a particle but rather a "quantum object" that sometimes has the properties of a wave and sometimes has the properties of a particle.

So "spacetime" is not exactly "space" added to "time", it is its own thing called spacetime and it has characteristics that can be discussed although discussing them in English leads to problems. The proper language of science is math and if you want to REALLY describe spacetime you're going to have to learn a lot of math.

 

[Fredrik]

Does that mean that the universe is 4 dimensions (space and time) and we are just 3 dimensional moving through the 4 dimensions of the universe? So things like rocks and cars and people are three dimensions and the universe is 4 dimensions?

A car is 3-dimensional, but its entire existence from when it's built to when it's destroyed, is 4-dimensional. If you want to understand this better, you should learn about spacetime diagrams (also called Minkowski diagrams).

Are things really 4 dimensions and we just don't see all of the dimensions?

Relativity doesn't say anything like that.

 

[Naty1]

I think this is just what Dr. Donis was saying.

Yes. It was supposed to be the same...Getting different descriptions, even though equivalent, is often needed to gain perspective...

I'll give you a rough analogy for space and time being considered 'spacetime' :

If you consider the ocean, say, one, and air the other, they seem pretty distinct, right? ...especially when it's flat calm... Easy to tell them apart...Then the wind picks up and waves are seen...where did the air go?? Now it's 'curved' too just like the surface of the water...[Space, time and spacetime also 'curves' by the way] then at around 50 or 60 mph, the surface of the water is picked up in a 'spume'...like rain droplets driven from the surface of the water...and it may extend three feet or more above the surface...you can no longer, perhaps, see the waves...'air and water' now have no clear boundary...they 'merge' into each other as if they maybe were a single entity...I've seen this a number of times when boating...and reading physics...

Well, in an analogous way, 'flexible' space and time also change from one to the other based on frames of reference [different observer perspectives]. Space and time 'conspire' together in such a mathematical form as to keep the speed of light the same for all observers.

By the way, if you start buying books, see Amazon Books or other online sources for less costly used copies...

 

[Naty1]

Strickland posts

I'm looking at some other threads and there is one by a guitar name about us moving through the 4 dimensional universe as fast as light.

BRAVO! I forgot to complement you on doing some searches... just about everything has been discussed numerous times. The trick is to figure out who knows what they are doing...the 'experts' I call them...and then you can just read those posts, because some threads go on and on and on...Few if anybody, I think, knows it ALL...

 

[Stricklandjr]

Your statement of the question "what is it?" is not helpful. "WHAT" something is is just a name we give it. In this case we give it the name "spacetime". There is no other answer to WHAT it is. Science is about describing the properties of the things we give names to and the properties of spacetime are discussed in general relativity.

A really excellent example of this terminology issue is the confusion that was experienced early in the days of quantum mechanics when people insisted on calling a photon either a "wave" or a "particle" because they were hung up on WHAT it is. In reality, a photon is NEITHER a wave nor a particle but rather a "quantum object" that sometimes has the properties of a wave and sometimes has the properties of a particle.

So "spacetime" is not exactly "space" added to "time", it is its own thing called spacetime and it has characteristics that can be discussed although discussing them in English leads to problems. The proper language of science is math and if you want to REALLY describe spacetime you're going to have to learn a lot of math.

Thank you Mr. phinds. I can handle it not knowing what spacetime really is as long as no one really knows, I just thought maybe everone here knows what spacetime is. I won't study on that one any more.

 

[Stricklandjr]

However, it's important to note that in all these models, the "object" (whether its an idealized point-like object or an object extended in space) is best viewed as its worldline or world tube. This is because of the relativity of simultaneity; different observers in different states of motion will "slice" 3-dimensional sections out of an extended object's world tube in different ways. So you can't really view the object as a 3-dimensional thing that moves through time; you have to look at its entire 4-dimensional world tube. When your cousin said that we live in 3 dimensions, he apparently wasn't taking that into account.

I wanted to come back to this because it really puts your finger on something really cool. In my drafting class we would picture a solid and then draw a line across it with arrows pointing in the direction for a cross-section view. We would do this for two or three different cross sections and label them Sec A-A, Sec B-B, Sec C-C, and so on. So you are telling me that we could imagine my rock extended into the 4th dimension of spacetime (not space, I'm getting that part now) and different people would see different cross sections of the 4 dimensional rock? What determines what their cross section view will be?

 

[Stricklandjr]

A car is 3-dimensional, but its entire existence from when it's built to when it's destroyed, is 4-dimensional. If you want to understand this better, you should learn about spacetime diagrams (also called Minkowski diagrams).


Relativity doesn't say anything like that.

First you said a cars existence is 4 dimensional just like Dr. Donis said. But then why did you say relativity doesn't say anything like that?

 

[PeterDonis]

So you are telling me that we could imagine my rock extended into the 4th dimension of spacetime (not space, I'm getting that part now) and different people would see different cross sections of the 4 dimensional rock?

For an appropriate sense of "see", yes. However, that appropriate sense of "see" is *not* the usual sense. What we are calling the 3-D "cross section" of a 4-D object is *not* what any observer actually sees, visually, because of the finite speed of light. Each 3-D cross section is really an abstract construction, not a direct observation.

What determines what their cross section view will be?

Their state of motion relative to the rock.

 

[PeterDonis]

First you said a cars existence is 4 dimensional just like Dr. Donis said. But then why did you say relativity doesn't say anything like that?

I think he was responding to the part where you said "we don't see all of the dimensions", which is indeed incorrect, as I (and others, I think) have already posted.

(Btw, I'm not actually a Dr. in either sense--medical or doctoral degree.)

 

[Stricklandjr]

I think he was responding to the part where you said "we don't see all of the dimensions", which is indeed incorrect, as I (and others, I think) have already posted.

(Btw, I'm not actually a Dr. in either sense--medical or doctoral degree.)

Thank you for clearing that up. And after looking at other threads you are definitely a Dr. of physics in my book.

 

[Stricklandjr]

For an appropriate sense of "see", yes. However, that appropriate sense of "see" is *not* the usual sense. What we are calling the 3-D "cross section" of a 4-D object is *not* what any observer actually sees, visually, because of the finite speed of light. Each 3-D cross section is really an abstract construction, not a direct observation.



Their state of motion relative to the rock.

Im going to try doing a drawing kind of like I would do in drafting class. I had to make it up in Paint since I don't have I-deas on my computer. I remember in jr. college physics drawing diagrams of things moving along the horizontal direction when time is changing so I hope this picture is kind of like you are talking about for a cross section view. Please tell me where I have gone wrong. I labeled the cross section as A-A like we did in drafting.

 

[Stricklandjr]

A car is 3-dimensional, but its entire existence from when it's built to when it's destroyed, is 4-dimensional. If you want to understand this better, you should learn about spacetime diagrams (also called Minkowski diagrams).

I have to thank you for that one Mr. Fredrik. I am now looking at the spacetime diagram subjects and you really put me on to something there. I should have done this before drawing that picture for Dr. Donis in the last post because I see it is not right. I can see that the world tube for someone in motion doesn't have the space direction perpendicular to his time direction. That's something I will have to really study on. How do you know how much to slant the space axis compared to the angle of the moving world tube?

 

[PeterDonis]

How do you know how much to slant the space axis compared to the angle of the moving world tube?

For 2-dimensional spacetime diagrams like the ones you're drawing (i.e., 1 dimension of space and 1 dimension of time), the space and time axes both make the same angle with the worldlines of light rays, which are 45-degree lines. So in your diagram, since the world tube of the person looking at the rock tilts up and to the right, the lines of simultaneity for that observer (i.e., the "slices" of the cross sections) will tilt to the right and up, so that they and the world tube are symmetrical about 45-degree lines going up and to the right.

 

[Fredrik]

How do you know how much to slant the space axis compared to the angle of the moving world tube?

See pages 5-8 in Schutz. (Especially fig. 1.4 on p. 8).

The early parts of that book should be readable even if you don't have much of a mathematical background. The book by Taylor & Wheeler is an alternative with less math.

 

[Stricklandjr]

See pages 5-8 in Schutz. (Especially fig. 1.4 on p. 8).

The early parts of that book should be readable even if you don't have much of a mathematical background. The book by Taylor & Wheeler is an alternative with less math.

Thank you Mr. Fredrik. I'm going to see about getting that book.

 

[Stricklandjr]

For 2-dimensional spacetime diagrams like the ones you're drawing (i.e., 1 dimension of space and 1 dimension of time), the space and time axes both make the same angle with the worldlines of light rays, which are 45-degree lines. So in your diagram, since the world tube of the person looking at the rock tilts up and to the right, the lines of simultaneity for that observer (i.e., the "slices" of the cross sections) will tilt to the right and up, so that they and the world tube are symmetrical about 45-degree lines going up and to the right.

I really think I am getting closer now. I put in a 45 degree line and then made the moving space direction the same angle and found the section A-A. But why is the light ray at 45 degrees and why did the moving guy's view slant to the same angle? Either you are beginning to make a genius out of me or else a little knowledge is going to be a dangerous thing for me. I'm studying on the spacetime diagram subject suggested by Mr. Fredrick and am seeing some things I have to study hard on before knowing enough to ask my next questions about what happened to the scaling of the distances when I rotated the moving guy's space direction.

 

[WannabeNewton]

The speed of the light ray is given by $\frac{\Delta x}{\Delta t} = 1$ implying $\frac{\Delta t}{\Delta x} = 1$ which is the slope of the light ray as depicted on the diagram. Recall that this is then equal to $\tan\theta$ where $\theta$ is the angle that the ray makes with the horizontal. $\tan\theta = 1\Rightarrow \theta = \frac{\pi }{4}$ in the first quadrant.

 

[PeterDonis]

I really think I am getting closer now. I put in a 45 degree line and then made the moving space direction the same angle and found the section A-A.

Yes, this looks correct.

But why is the light ray at 45 degrees

Because we are using units in which the speed of light is 1; for example, if the space axis is in meters, the time axis is in meters of light-travel time, i.e., one unit of time is about 3.3 nanoseconds, since that's the time it takes for light to travel 1 meter. (Or we could have time in seconds and space in light-seconds = 300,000 km, or time in years and space in light-years; whatever is appropriate to the problem.) I slipped those units in on you without telling you. But those are the most commonly used units in relativity, so it's good to get used to them.

and why did the moving guy's view slant to the same angle?

There are several ways to answer this, but it basically comes down to the fact that that's what makes the math work consistently. The reason it has to be different from the ordinary Euclidean case, where the two axes stay perpendicular, is that there is a minus sign in the spacetime interval formula; this is the spacetime analog to the Pythagorean theorem:

s^2 = x^2 - c^2 t^2

Notice the minus sign, where in the ordinary Pythagorean theorem we have a plus sign: s^2 = x^2 + y^2. The minus sign leads to a number of key differences from the Euclidean case, and the way the space axis tilts for a moving observer is one of them.

 

[Stricklandjr]

The speed of the light ray is given by $\frac{\Delta x}{\Delta t} = 1$ implying $\frac{\Delta t}{\Delta x} = 1$ which is the slope of the light ray as depicted on the diagram. Recall that this is then equal to $\tan\theta$ where $\theta$ is the angle that the ray makes with the horizontal. $\tan\theta = 1\Rightarrow \theta = \frac{\pi }{4}$ in the first quadrant.

Got it. This is really important. I'm going to mull this over a lot. The 4 dimensional light ray is always at 45 degrees from time and space directions. Now it's really getting in touch with nature and the scheme of things. Lot's of thinking to do. Thanks a lot Mr. WannabeNewton (you must already be a Newton).

 

[WannabeNewton]

Thanks a lot Mr. WannabeNewton

Haha it sounds so awkward when you call me Mr because I'm still a young'un. You can call me scrappy

(you must already be a Newton).

Sadly, a feat only Newton himself could achieve

 

[Stricklandjr]

Yes, this looks correct.

Thanks only to you and the others.

Because we are using units in which the speed of light is 1; for example, if the space axis is in meters, the time axis is in meters of light-travel time, i.e., one unit of time is about 3.3 nanoseconds, since that's the time it takes for light to travel 1 meter. (Or we could have time in seconds and space in light-seconds = 300,000 km, or time in years and space in light-years; whatever is appropriate to the problem.) I slipped those units in on you without telling you. But those are the most commonly used units in relativity, so it's good to get used to them.

I'm really starting to get on to this. But I am overwhelmed with the idea that the universe is organized with the ray of light always at the 45 degree angle for the guy with perpendicular time and space directions and that the time and space angles for the moving guy are the same on either side of the light ray. That just seems really awesome for some reason I can't really fathom right now. I can see how the moving world tube must be slanted due to its speed, but then for the moving guys space direction in spacetime to know just how much to rotate up to make those angles equal is something I will study very long and hard on.

There are several ways to answer this, but it basically comes down to the fact that that's what makes the math work consistently. The reason it has to be different from the ordinary Euclidean case, where the two axes stay perpendicular, is that there is a minus sign in the spacetime interval formula; this is the spacetime analog to the Pythagorean theorem:

s^2 = x^2 - c^2 t^2

Notice the minus sign, where in the ordinary Pythagorean theorem we have a plus sign: s^2 = x^2 + y^2. The minus sign leads to a number of key differences from the Euclidean case, and the way the space axis tilts for a moving observer is one of them.

O.K. Dr. Donis I will really start studying on this because it seems like a really big point in all this. I will even get out my algebra book and review the Pythagorean theorem.

One question I have is it looks like when I try to follow the internet articles on spacetime diagrams that something strange is going on with the scaling of space distances between perpendicular directions for time and space compared to the slanted moving guy's distances. I notice the length is different for different cross sections like they are in drafting. Is that really what happens?

 

[Fredrik]

something strange is going on with the scaling of space distances between perpendicular directions for time and space compared to the slanted moving guy's distances. I notice the length is different for different cross sections like they are in drafting. Is that really what happens?

Check out page 15 in Schutz. Curves on which $-t^2+x^2$ is constant look the same in all coordinate systems. So if you pick a point on the t axis that's 1 second away from the origin, and follow such a hyperbola from that point to the point where it intersects the t' axis, you have found an event that is 1 second away from the origin in the other coordinate system.

 

[Stricklandjr]

Check out page 15 in Schutz. Curves on which $-t^2+x^2$ is constant look the same in all coordinate systems. So if you pick a point on the t axis that's 1 second away from the origin, and follow such a hyperbola from that point to the point where it intersects the t' axis, you have found an event that is 1 second away from the origin in the other coordinate system.

Thank you Fredrik. I used up my previewing on Schutz before getting through that but I get an inkling of what it is so I'm going to put your formula into an Excel spread sheet and graph it out. I've also been starting to look in my algebra book and am going to study the hyperpola. I never thought I liked math but now I'm beginning to think it might be cool after all if it can show me how the universe works.

 

[Stricklandjr]

same time in spacetime

OK. You guys got me doing more homework than I ever did in jr. college physics and algebra classes. But this is really getting to be neat stuff. I feel like I'm being a physicist. So I played around with the hyperbola graphs in Microsoft Excel and came up with this one after going thru Shutz and going back to some things Dr. Donis said about slices and came up with a slice. What's amazing is how the slice explains why the moving guy sees an earlier time on my clock world tube (don't worry I know that you have to take into account how much time it takes for light to get there before you can see and I don't care about that right now because these basic ideas are what's really got my brain spinning). You were really putting me in the right direction Mr. Fredrick when you said to dig into spacetime pictures thank you.

I marked times t1 t2 and t3 to show these times are all the same since they are on the hyperbola. t4 is the time on my world tube clock that the moving guy would see in his slice of 4dimensional spacetime that Dr. Donis told me about. I really used ct for the time axis to get the units suggested by Mr. Fredrik.

Now I can't say this for sure but it looks like the space direction for the moving guy is always going to be a tangent line to the hyperbola.

 

[Stricklandjr]

I'm really have to study hard on something now because something don't seem right here. On the one hand people here are saying that I am moving along the 4th direction all the time. But when I look at the spacetime diagram then nothing is moving because everything is a 4 dimension world tube and the tubes are not moving anywhere. So was my thinking all wrong? Maybe the spacetime is 4 dimensions and I am 3 dimensional moving through the 4 dimensional spacetime? I'm reall sorry for getting this mixed up after I thought I was really getting it but now it looks like the world tubes can't be moving.

I still remember what Dr. Donis said: So you can't really view the object as a 3-dimensional thing that moves through time; you have to look at its entire 4-dimensional world tube"

But how do we move through time? It seems like I can feel myself moving through time but when I look at my world tube it doesn't move.

 

[PeterDonis]

it looks like the space direction for the moving guy is always going to be a tangent line to the hyperbola.

Yes, that's correct. You can actually prove this mathematically.

 

[PeterDonis]

I'm really have to study hard on something now because something don't seem right here. On the one hand people here are saying that I am moving along the 4th direction all the time.

For an appropriate sense of the term "moving", yes. See below.

But when I look at the spacetime diagram then nothing is moving because everything is a 4 dimension world tube and the tubes are not moving anywhere.

Yes, that's right. What you have here are two different ways of looking at the same physics:

If you are trying to make sense of what a person following a particular worldline/world tube is experiencing, you have to have some way of talking about his experience of "moving" through time--he doesn't experience his entire 4-dimensional world tube all at once. So you have to talk about things like 3-D cross sections, bearing in mind that these are abstractions, and only approximate ones at that.

But if you are looking at the entire spacetime history, for example when you draw a spacetime diagram, you are looking at the entire 4-dimensional thing all at once. On this view, as you say, nothing "moves" at all; the entire 4-dimensional thing is just there.

Both of these views are correct; they are, as I said above, just different ways of looking at the same physics. As far as what things are "really like", I (and many others here) would say that's a question of philosophy, not physics.

 

[Stricklandjr]

For an appropriate sense of the term "moving", yes. See below.



Yes, that's right. What you have here are two different ways of looking at the same physics:

If you are trying to make sense of what a person following a particular worldline/world tube is experiencing, you have to have some way of talking about his experience of "moving" through time--he doesn't experience his entire 4-dimensional world tube all at once.

I probably don't understand this Dr. Donis. I feel like I have let you down after all of the knowledge you and Mr. Fredrik have offered me. Does it me he is really a 4 dimensional world tube but he just experiences one slice at a time?

So you have to talk about things like 3-D cross sections, bearing in mind that these are abstractions, and only approximate ones at that.

I am afraid I don't know what this abstraction is. I'm sorry to disappoint you. I think I understand cross sections though.

But if you are looking at the entire spacetime history, for example when you draw a spacetime diagram, you are looking at the entire 4-dimensional thing all at once. On this view, as you say, nothing "moves" at all; the entire 4-dimensional thing is just there.

Yes. You are saying it just like I was trying to. The entire 4 dimensional thing is just there. So I still need to understand how it could be moving.

Both of these views are correct; they are, as I said above, just different ways of looking at the same physics.

I'm sorry for being slow and don't mean to repeat but are the two ways, one way is a 3 dimensional guy moves through spacetime and the other way is the guy is a 4 dimensional world tube. But it seems like if its a 3 dimensional guy moving through spacetime then the slices don't work anymore but if it's a 4 dimensional world tube nothing can move.

As far as what things are "really like", I (and many others here) would say that's a question of philosophy, not physics.

Are you saying that you physicists can't know what it's really like and I have to study philosophy to know what is really going on with the universe? My cousins buddy told me I was too dumb to understand the universe and it's beginning to look like he might be right. I guess I'm getting out of my element. My daddy told me if things didn't work out I could come back to the farm. But I know I don't want to do philosophy, they would have me trying to dance on the head of a pin.

 

[PeterDonis]

Does it me he is really a 4 dimensional world tube but he just experiences one slice at a time?

No, it means that the question of what he "really is" is a philosophical question, not a scientific one. (At least, IMO it is.) See further comments below.

I am afraid I don't know what this abstraction is.

Sorry, I should have been clearer. What I mean is that, as I said in a previous post, the cross section is not something anyone directly observes, because of light speed time delay. We experience objects as 3-D things that move in space and exist for some length of time, but our brains construct that experience from the actual data; the actual data is the light that we receive from objects, and that light is time delayed. It's just that the time delay, under ordinary conditions, is much, much smaller than any length of time we can consciously perceive, or even that our nervous systems can detect.

For example, if an object is 1 meter long, it takes light 3.3 nanoseconds to travel the length of the object, so the light you are seeing at a given instant from the object's far side was emitted 3.3 nanoseconds before the light you are seeing at the same instant from the object's near side. But your neurons have a cycle time of something like 20 milliseconds, more than a million times longer than that 3.3 nanoseconds, and you can only consciously perceive time intervals of around 100 milliseconds or longer, almost ten million times longer than that 3.3 nanoseconds.

So under ordinary conditions the light speed time delay is undetectable. But it's still there, and that means that the 3-D cross sections in our mathematical model are not directly observed; we have to construct them by extrapolating forward from the time-delayed light signals we receive. The same goes for the 4-dimensional world tubes in general; we don't directly observe them, we have to construct them in our mathematical models based on the data we have.

Yes. You are saying it just like I was trying to. The entire 4 dimensional thing is just there. So I still need to understand how it could be moving.

It isn't. If you view an object as its entire 4-dimensional world tube, it doesn't move; it's just there. But you don't experience it that way, so if you want to talk about your experience--and after all, if we're going to talk about experimental results, we have to talk about our experiences of them--you can't just talk about 4-dimensional things that are just there, because that's not what we experience. You have to talk about things moving, since that's what we experience; and that means you have to have a second way of looking at the physics, in addition to the 4-dimensional way, if for no other reason than to be able to translate what the 4-dimensional model says into predictions about what people will actually experience.

it seems like if its a 3 dimensional guy moving through spacetime then the slices don't work anymore but if it's a 4 dimensional world tube nothing can move.

The two ways are not two different ways the world can be, one of which is true and one of which is false. Both ways are valid; they are just different ways of looking at the same physics, as I said before.

Are you saying that you physicists can't know what it's really like

No; physicists are not limited to considering just physics questions, any more than anyone else is. And even if knowing the physics doesn't necessarily tell you "what it's really like", knowing the physics is certainly not irrelevant.

and I have to study philosophy to know what is really going on with the universe?

That depends on your attitude towards philosophy. My personal view is that the only thing that studying philosophy will do for you is to help inoculate you against the claims of philosophers to "know what is really going on". IMO, *nobody* knows what is "really going on"; how could we expect to? It's a wonder we know as much as we do. But maybe that's just me.

At any rate, the main point I was really making is that PF is a forum for discussing physics, not philosophy; so when people start trying to talk on PF about "what is really going on", as opposed to actual physical theories or actual experimental results, the discussion quickly gets bogged down. It's better to focus on the actual theories and the actual experiments.

My cousins buddy told me I was too dumb to understand the universe and it's beginning to look like he might be right.

I suspect your cousin's buddy is in worse shape than you on that score; at least you came here and asked intelligent questions.

I guess I'm getting out of my element.

Don't give up too easily. This stuff is counterintuitive; it's not supposed to just instantly ring true to you. It didn't to me at first either. I've been studying this stuff for many years; so have most of the experts here.

But I know I don't want to do philosophy, they would have me trying to dance on the head of a pin.

As you can see from the above, I agree with you. But you should realize that avoiding philosophy, which is IMO a good idea, also means avoiding questions that we all feel an urge to ask but which don't have any real meaning if you're avoiding philosophy, like "what is it *really* like?"

 

[Fredrik]

Does it me he is really a 4 dimensional world tube but he just experiences one slice at a time?

An object's entire existence is something 4-dimensional. Specifically, it's a bunch of curves in spacetime that describe the object's motion. Each curve describes the motion of a component particle. But if I mention my car, you won't assume that I'm referring to a set of timelike curves in a 4-dimensional spacetime. You will assume that I'm referring to the 3-dimensional thing that's parked outside my house right now. "Now" is the key word here. "Space, right now" is a 3-dimensional slice of spacetime. My car's entire existence is represented by a set of curves. But my car (and by that I mean "my car, right now") is represented by the set of points where those curves intersect that slice. That's a 3-dimensional region of spacetime.

Note that in a spacetime diagram, the slices that we can think of as "space, at time t" are horizontal lines. The world tube you've drawn will intersect those slices at different x coordinates. In relativity, that's what motion is, nothing more, nothing less.

Are you saying that you physicists can't know what it's really like and I have to study philosophy to know what is really going on with the universe?

Yes to the first part, and no to the second part. Physicists don't always know what things are really like, but when they don't, philosophers don't either. Physicists do experiments to find out how accurate a theory's predictions are. This way they can eliminate the bad theories. But a theory may be consistent with more than one idea about "what's really going on", and in that case, no one will know what's really going on. Each attempt to interpret a theory is philosophy, and the thought process that you have to go through to understand that is philosophy.

Oddly enough, this doesn't mean that physicists who want to understand these things better can just pick up a philosophy book.

 

[TheBC]

.Always interesting to read what Einstein himself was thinking of all this:

<< From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world". >> Albert Einstein. "Relativity: The Special and the General Theory." 1916. Appendix II Minkowski's Four-Dimensional Space ("World") (supplementary to section 17 - last section of part 1 - Minkowski's Four-Dimensional Space).

<< Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. >> Albert Einstein, "Relativity", 1952.

 

[Stricklandjr]

.Always interesting to read what Einstein himself was thinking of all this:

<< From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world". >> Albert Einstein. "Relativity: The Special and the General Theory." 1916. Appendix II Minkowski's Four-Dimensional Space ("World") (supplementary to section 17 - last section of part 1 - Minkowski's Four-Dimensional Space).

<< Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. >> Albert Einstein, "Relativity", 1952.

Boy! Mr. TheBC you are really giving us some real important sayings of Einstein. It seems like he really did think that the universe and things are 4 dimensional all there at once. I think this is very big news and Mr. Fredrik and Dr. Donis will really be interested to hear about this. You have made some very important information to our discussion.

I think maxverywell could really use your knowledge on his post because he had some of the same puzzling about moving in time and the 4 dimensional universe.

 

[Stricklandjr]

Other Theory

I was trying to go back through the information given by Mr. Fredrik and Dr. Donis to know more about why they wouldn't agree that what Einstein said. I mean they really agreed but had to say that you couldn't know it for sure because the real 4 dimensional universe with slices is philosophy. One thing I saw in Mr. Fredrik's information was that it may not be real because there is another theory that says it is not really a 4 dimensional universe all there at once.

Mr. Fredick pointed out that: "But a theory may be consistent with more than one idea about "what's really going on", and in that case, no one will know what's really going on."

But he didn't say what the other idea is that would be different from the 4 dimensional universe all there at once. What is the other theory?

 

[PeterDonis]

I think this is very big news and Mr. Fredrik and Dr. Donis will really be interested to hear about this.

I'm well aware of these sayings of Einstein, thank you. I'm sure Fredrik is too. Bear in mind that Einstein in those passages was not talking about the physics; he was talking about his interpretation of the physics. In other words, what he was saying was really philosophy, not physics. His philosophy is certainly consistent with the physics, but it's still philosophy.

 

[Fredrik]

...the real 4 dimensional universe with slices is philosophy. One thing I saw in Mr. Fredrik's information was that it may not be real because there is another theory that says it is not really a 4 dimensional universe all there at once.

Mr. Fredick pointed out that: "But a theory may be consistent with more than one idea about "what's really going on", and in that case, no one will know what's really going on."

But he didn't say what the other idea is that would be different from the 4 dimensional universe all there at once. What is the other theory?

The 4-dimensional spacetime is part of the definition of SR, so this is not the sort of thing I had in mind. I was thinking about attempts to get something out of the theory that isn't really there. For example, the theory says that if your twin goes on a space voyage and travels close to the speed of light relative to the Earth, he will be significantly younger than you when he gets back. SR tells you how to calculate his final age and your final age, but it doesn't tell you why the calculations should be done that way. Someone who wants to explain it could try to say things like this:

a) Space is filled up with a substance called the ether. Clocks at rest relative to the ether tick at their maximum ticking rates. A clock moving with velocity v relative to the ether is slow by a factor of $\gamma=1/\sqrt{1-v^2}$ because of its interactions with the ether. An observer equipped with such a clock will still measure the speed of light to be 1, because every object that's comoving with him (in particular the meter stick he uses to measure distances) will be contracted by a factor of $\gamma$ due to interaction with the ether.

b) Motion doesn't affect the ticking rate of clocks at all. There is simply "less time" to be accumulated along the astronaut twin's path through spacetime from the departure event to the return event.

I would say that b) is the natural and straightforward interpretation of SR, and that a) is an old-fashioned idea that shouldn't be encouraged. But it would be unscientific of me to say that b) is correct and a) is wrong, because neither of these assumptions has any falsifiable consequences. So there's no experiment that can support that claim.

 

[PeterDonis]

I mean they really agreed but had to say that you couldn't know it for sure because the real 4 dimensional universe with slices is philosophy.

...

What is the other theory?

Fredrik has given a good response, but I'd like to give a few other reasons why I am careful about making claims about what things are "really like":

(1) We know that special relativity is only an approximate theory; it is only strictly valid in the complete absence of gravity, and in the universe we observe there is gravity present everywhere to some extent. So the Minkowski spacetime that we use in SR is certainly not an exactly correct model of what things are "really like".

(2) The obvious response to #1 is that general relativity, which does deal with gravity, also uses 4-dimensional spacetime; it just allows that spacetime to be curved, whereas SR assumes that it is flat. However, we know that GR is not a complete theory, because it doesn't include quantum mechanics. And once we include quantum mechanics, it is highly likely that the concept of "spacetime" as we use it in GR is no longer fundamentally valid--that at some very small scale, of the order of the Planck length/Planck time, our model of spacetime as a smooth 4-dimensional manifold will break down. So even the general curved spacetime that we use in GR might not be an exactly correct model of what things are "really like".

(3) Even if we ignore #1 and #2, there is still a big problem with making claims about the entire universe based on 4-dimensional spacetime models. When we talk about a made up scenario, we stipulate what is in it. We can draw a spacetime diagram that contains everything that is in the scenario, as far in the past or future as we like, extended as far in space as we like, because we made up the scenario so we get to declare by fiat what is in it.

But in the real universe, we can't do that. People talk about what is happening in the Andromeda galaxy, say, "right now", as if it were something we knew directly, or at least something that is such an obvious, certain extrapolation from what we know directly that it's basically the same thing. But it isn't. The best information we have from the Andromeda galaxy, the light that is just now reaching us from there, is 2 million years out of date. Lots of things could have happened there that we don't know about. I don't just mean that stars could have exploded, another galaxy could have collided with it (from the "back side", the side we can't see), or aliens could have taken it over and rearranged all the stars in an orderly square array. I mean that, say, some quantum phenomenon could have changed the very nature of "reality" there--say some kind of phase transition similar to the ones that happened in the early universe--so that 4-dimensional spacetime is no longer even a good model of it any more.

But, you say, surely that sort of thing can't happen? Well, it seems highly unlikely based on what we currently know. But what we currently know is extremely limited. It doesn't seem that way to us because we've expanded our knowledge so much in the recent past. But that just means we've gone from being colossally ignorant to just being extremely ignorant. So when I see people, even physicists, proclaiming that "the universe is a 4-dimensional manifold that exists all at once" as though it were a proven fact, or the next thing to it, I just sigh and remind myself that even very smart people can have trouble distinguishing what is known from what is just speculation--reasonable speculation, speculation that's consistent with what we know, but still speculation.

 

[Stricklandjr]

Lorentz Ether Theory

Mr. Fredrik and Dr. Donis I understand now that you both already knew about what Einstein said and that he was not saying it as a physicist but was being a philosopher. You have both pointed out many things so I have to study some more on all that.

Please do not think I am starting an argument because you two have taught me much about relativity but one thing I noticed when Mr. Fredrik was telling about two theories: a) ether theory and b) 4 dimensional universe all there at once. I don't think ether theory could be used to call Einstein's statements into disrepute because of what I read the other day when I signed up in the physics forum and agreed to the rules given by Mr. Greg Bernhardt. Mr. Greg Bernhardt said: "Generally, in the forums we do not allow the following:

Attempts to promote or resuscitate theories that have been discredited or superseded (e.g. Lorentz ether theory);

So I don't think ether theory should be used on this forum to contradict Einstein."