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

In summary, photons are real, physical entities that must have a relationship with the fourth dimension and therefore have some velocity relative to it. The equation x4=ict, used in Einstein's theory of relativity, shows that the fourth dimension moves at the speed of light relative to the three spatial dimensions. This means that the velocity of every object, including photons, through the four-dimensional spacetime manifold is c, except for photons which follow null worldlines and do not have a well-defined 4-velocity. The photon is stationary relative to the fourth dimension and tracks its movement. The fourth dimension is a real, physical entity that can bend, curve, and move. The question of how the photon moves relative to the fourth dimension requires a
  • #1
AstroMath
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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!
)
 
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  • #2
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
Ibix said:
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..

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
Ibix said:
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..

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
AstroMath said:
So then how does the photon move relative to the fourth dimension?

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
Think about it this way.

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

https://www.amazon.com/dp/B00R86QABW/?tag=pfamazon01-20
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?




 
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  • #7
Markus Hanke said:
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.

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
Markus Hanke said:
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.

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

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.

AstroMath said:
Does the above logic make sense to you?

No, because for photons you have ##ds^2=0##.
 
  • #11
Ibix said:
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?

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
Markus Hanke said:
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##.

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
  • #14
Ibix said:
C, as I have said already.

I now recall your previous thread:
https://www.physicsforums.com/threads/einsteins-relativity-of-simultaneity-quantum-paradox.878302/
Also, you have been told this all before:
Stanford: objects in spacetime all move at constant speed c?
I am not willing to spend more time saying the same thing over and over again to you - you will simply refuse to accept it and it is a waste of both our time. I'm out.

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

Thos thread is closed.
 

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

1. What is the fourth dimension?

The fourth dimension is a theoretical concept in physics that refers to a spatial dimension beyond the three dimensions of length, width, and height. It is often denoted as x4 and is thought to be a direction perpendicular to all three of the known dimensions.

2. How is the velocity of a photon measured?

The velocity of a photon can be measured by dividing the distance it travels by the time it takes to travel that distance. This is known as the speed of light, which is approximately 299,792,458 meters per second in a vacuum. This is considered to be the upper limit for the velocity of a photon.

3. Can a photon really travel through the fourth dimension?

The concept of a photon traveling through the fourth dimension is purely theoretical and has not been proven. It is based on the idea that a photon does not experience time and therefore could potentially travel through the fourth dimension, which is often associated with time. However, this is still a topic of debate and further research is needed.

4. How does the velocity of a photon in the fourth dimension compare to its velocity in the other dimensions?

Since the fourth dimension is a theoretical concept, it is difficult to determine the exact velocity of a photon in this dimension. However, some theories suggest that the velocity of a photon in the fourth dimension may be different from its velocity in the other dimensions. It is also possible that the concept of velocity may not even apply in the fourth dimension.

5. What implications would a photon traveling through the fourth dimension have on our understanding of physics?

If it were proven that a photon can travel through the fourth dimension, it would have significant implications on our understanding of physics. It would challenge our current theories and could potentially lead to a better understanding of the universe and its dimensions. However, until this concept is further explored and evidence is found, it remains a theoretical concept.

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