# I What is the velocity of the photon through the fourth dimension x4?

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1. Jul 20, 2016

### AstroMath

What is the velocity of the photon through the fourth dimension x4?

Photons are real, physical entities.

The fourth dimension is a real, physical entity.

Therefore, photons must have a relationship with the fourth dimension. They must have some velocity relative to it.

What is the velocity of the photon through the fourth dimension x4?

Do you agree with the following:

1. Maxwell/Einstein teach that light has the velocity c through the three spatial dimensions.
2. Relativity teaches us that the velocity of every object is c through the four-dimensional spacetime manifold.
3. If a photon has a velocity other than zero relative to the fourth dimension, then either #1 or #2 above would no longer be true.
4. As #1 and #2 must always be true, a photon must remain stationary relative to the fourth dimension.
5. As a photon is stationary relative to the fourth dimension, it tracks and traces x4's movement. The fourth dimension is moving at c relative to the three spatial dimensions.
Remarkably, this is exactly what Einstein/Minkowski taught with x4=ict which means dx4/dt=ic -- the fourth dimension is moving at c relative to the three spatial dimensions.

Einstein's GR taught us that dimensions could bend, curve, and move and so does dx4/dt=ic.

Does the above logic make sense to you?

What, in your opinion, is the velocity of the photon through the fourth dimension x4?

(HINT:
Consider the equation x4=ict.
When t=1, what is x4? When t=2, what is x4? When t=3, what is x4? What happens to x4 as the seconds on your watch tick by? In three seconds, how far has x4 moved? 3*ic meters!
)

Last edited: Jul 20, 2016
2. Jul 20, 2016

### Ibix

2 only applies to massive objects, which move on time-like worldlines. It is not true for light, which follows null worldlines. 4-velocity is not well defined on null worldlines since the proper time along them is zero and you can't differentiate with respect to it..

3. Jul 20, 2016

### AstroMath

You write that the following is not true for light: "Relativity teaches us that the velocity of every object is c through the four-dimensional spacetime manifold."

So are you saying that "Relativity teaches us that the velocity of every object is c through the four-dimensional spacetime manifold, except for light, which does not travel at c through the four-dimensional spacetime manifold."

Are you saying that everything travels at the velocity of light, except for light?

How fast does light travel through spacetime, in your opinion?

4. Jul 20, 2016

### AstroMath

What is the photon doing relative to the fourth dimension? How does a photon move relative to the fourth dimension? Are you saying we cannot answer this? Do you agree that the photon is a real, physical entity? Do you agree that the fourth dimension is a real, physical entity? So then how does the photon move relative to the fourth dimension?

5. Jul 20, 2016

### Markus Hanke

When you go to work/school tomorrow morning, how will you move relative to time ? What does that even mean ? Do you mean how much time will it take you to get to where you are going ? Or something else ?

You need to make your question mathematically and physically precise, then we'll try to answer it.

6. Jul 20, 2016

### AstroMath

x4=ict appears in all of Einstein's books on relativity including:

https://www.amazon.com/Relativity-S...TF8&qid=1468994806&sr=8-2&keywords=relativity
The Meaning of Relativity
The Meaning of Relativity: Four Lectures Delivered at Princeton University, 1921
Einstein's 1912 Manuscript on the Special Theory of Relativity

The spacetime metric afforded and exalted by x4=ict offers a more concise way of expressing all of relativity than do Einstein’s two postulates, as both the constancy of c and Galilean relativity follow directly from the metric. Do not take my word for it. The great mathematician Herman Weyl says as much in his epic 1918 book Space, Time, Matter:

The solution of Einstein, which at one stroke overcomes all difficulties, is then this: the world is a four-dimensional affine space whose metrical structure is determined by a non-definite quadratic form Q(x) = (xx) which has one negative and three positive dimensions. All physical quantities are scalars and tensors of this four-dimensional world, and all physical laws express invariant relations between them. --Weyl, Hermann. Space, Time, Matter (Dover Books on Physics) (Kindle Locations 4083-4087). Dover Publications. Kindle Edition

Consider the equation x4=ict.
When t=1, what is x4? When t=2, what is x4? When t=3, what is x4? What happens to x4 as the seconds on your watch tick by? How fast does it move?

Last edited by a moderator: May 8, 2017
7. Jul 20, 2016

### AstroMath

I made the question *perfectly* precise. It is you who are not being precise. Please share, precisely, what you do not agree with/do not understand about my question:

What is the velocity of the photon through the fourth dimension x4?
Photons are real, physical entities.
The fourth dimension is a real, physical entity.
Therefore, photons must have a relationship with the fourth dimension. They must have some velocity relative to it.
What is the velocity of the photon through the fourth dimension x4?
Do you agree with the following:
1. Maxwell/Einstein teach that light has the velocity c through the three spatial dimensions.
2. Relativity teaches us that the velocity of every object is c through the four-dimensional spacetime manifold.
3. If a photon has a velocity other than zero relative to the fourth dimension, then either #1 or #2 above would no longer be true.
4. As #1 and #2 must always be true, a photon must remain stationary relative to the fourth dimension.
5. As a photon is stationary relative to the fourth dimension, it tracks and traces x4's movement. The fourth dimension is moving at c relative to the three spatial dimensions.
Remarkably, this is exactly what Einstein/Minkowski taught with x4=ict which means dx4/dt=ic -- the fourth dimension is moving at c relative to the three spatial dimensions.
Einstein's GR taught us that dimensions could bend, curve, and move and so does dx4/dt=ic.
Does the above logic make sense to you?
What, in your opinion, is the velocity of the photon through the fourth dimension x4?​

8. Jul 20, 2016

### AstroMath

I can tell you exactly how I am moving relative to the fourth dimension, depending on the velocity of the vehicle I drive to school.

Do you not agree with this?

Or do you think it is impossible to know? Have you studied Einstein's relativity perchance?

Please do not project your ignorance of relativity upon my question. Thanks! :)

9. Jul 20, 2016

### Ibix

I already pointed out precisely where your argument went wrong. A different way to look at this is to note that the interval along a null worldline is zero (hence why it's called null). Velocity is, loosely, distance over time. In this case, the "distance" is the interval and is zero. How could velocity be c?

10. Jul 20, 2016

### Markus Hanke

The world lines of photons are null geodesics, so you cannot parametrise them with proper time. The separation between any two neighbouring events on a null geodesic is zero, hence the name. As such, the concept of 4-velocity is not defined for photons.

No, because for photons you have $ds^2=0$.

11. Jul 20, 2016

### AstroMath

So are you saying that the velocity of a photon through spacetime is 0? Or are you saying that the velocity of the photon through space is 0? Or are you saying that the velocity of the photon through x4 is zero?

Again, I ask, "What is the velocity of the photon relative to x4?" Are you saying it is zero? What is it in your opinion?

This is a very simple question: "What is the velocity of the photon relative to x4?"
a) 0
b) c
c) undefined
d) none of the above

12. Jul 20, 2016

### AstroMath

Yes, the 4-velocity may indeed not be defined! I agree!

But how is a photon moving relative to the fourth dimension?

Do you agree that photons are real, physical entities?

Do you agree that the fourth dimension is a real, physical entity?

Do you agree that the photon moves at c relative to the three spatial dimensions?

Again, I ask, "What is the velocity of the photon relative to x4?" Are you saying it is zero? What is it, in your opinion?

This is a very simple question: "What is the velocity of the photon relative to x4?"
a) 0
b) c
c) undefined
d) none of the above

13. Jul 20, 2016

### Ibix

14. Jul 20, 2016

### AstroMath

So you are saying that the photon moves at c through the fourth dimension x4?

And a photon also moves at c through the three spatial dimensions, as attested to by Maxwell and Einstein's second postulate of relativity.

Ergo, you are saying that light not only has the veloicty of c through the three spatial dimensions, but it also has a velocity of c through the fourth dimension x4.

Praytell, when you combine these velocities, what is the total magnitude of the velocity of light through spacetime?

Consider the equation x4=ict.
When t=1, what is x4? When t=2, what is x4? When t=3, what is x4? What happens to x4 as the seconds on your watch tick by? In three seconds, how far has x4 moved? 3*ic meters!

15. Jul 20, 2016

### Staff: Mentor

How many different ways of saying "undefined" are there?