Quantum interpretation of three polarizers - Revision history

Ist12916 at 08:33, 15 May 2025

2025-05-15T08:33:43Z

Ist12916 at 20:49, 1 January 2025

2025-01-01T20:49:25Z

Ist12916 at 10:52, 31 December 2024

2024-12-31T10:52:31Z

Ist12916 at 10:10, 31 December 2024

2024-12-31T10:10:07Z

Ist12916 at 10:05, 31 December 2024

2024-12-31T10:05:43Z

Ist12916 at 14:07, 28 December 2024

2024-12-28T14:07:29Z

Ist12916 at 13:28, 28 December 2024

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Ist12916 at 09:16, 28 December 2024

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Ist12916 at 09:15, 28 December 2024

2024-12-28T09:15:36Z

Ist12916 at 09:10, 28 December 2024

2024-12-28T09:10:30Z

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-[[File:Data Analise Polaroid.png|240|thumb| If we run the experiment for at least 90º of rotation is clear that we can expect a probability for a photon to pass a polarizer proportional to a sinusoidal function as in the orthogonal state no photon can pass. By the contrary in an aligned stat the probability to pass is 100%.]]
+[[File:Data Analise Polaroid.png|240|thumb| If we run the experiment for at least 90º of rotation is clear that we can expect a probability for a photon to pass a polarizer proportional to a sinusoidal function as in the orthogonal state no photon can pass. By the contrary, in an aligned stat the probability to pass is 100%.]]
 If we conduct the [[Light_Polarization|Polaroid]] experiment by doing a 180° scan, we will observe that the photons' probability of passage/transmission is proportional to a sinusoidal function, like a <math> sin^2(\theta)</math>. The sinus has to be squared as any probability can't be negative. Note that <math> sin^2(\theta)</math> is still a sinusoidal function.
 Let's describe the polarization state of light as a two-dimensional vector, as illustrated in the figure. Vertically polarized light corresponds to a vector pointing upwards (0, 1), horizontally corresponds to (1,0). We use Dirac notation to represent these vectors, ''|V>'' and ''|H>'' respectively. An arbitrary vector can be written as \(|α〉=cos⁡(α) |V〉+ sin(⁡α) |H〉 \).

@@ Line 47: / Line 47: @@
 '''Key Points of Clarification:'''
-*The photon does not ''keep'' its original polarization if it passes through; rather, it becomes aligned with the polarizer axis.
+*The photon does not ''keep'' its original polarization state if it passes through; rather, it becomes a new state aligned with the polarizer axis.
-*The outcome is probabilistic: a photon may or may not pass a polarizer, based on the projection of its initial polarization onto the polarizer's axis.
+*The outcome is probabilistic: a photon may or may not pass a polarizer, based on the projection of its initial polarization sate onto the polarizer's axis.
 *This phenomenon underscores the quantum mechanical principles of state collapse and measurement, distinct from classical wave explanations.

@@ Line 10: / Line 10: @@
 <math>
-〖Prob=|〈V|P_{(45°)} |V〉|〗^2=1/2
+Prob=|〈V|P_{(45°)} |V〉|^2=1/2
 </math>

@@ Line 29: / Line 29: @@
 </math>
-where \(Δθ=Frac{90º}{(N−1)}\)
+where \(Δθ=\frac{90º}{(N−1)}\)
 This simplifies to:

← Older revision		Revision as of 10:05, 31 December 2024
Line 1:		Line 1:
−	[[File:Data Analise Polaroid.png\|240\|thumb\| If we run the experiment for at least 90º of rotation is clear that we can expect a probability for a photon to pass a polarizer proportional to a sinusoidal function as in the orthogonal state no photon can pass ~~and~~ in an aligned stat the probability is 100%.]]	+	[[File:Data Analise Polaroid.png\|240\|thumb\| If we run the experiment for at least 90º of rotation is clear that we can expect a probability for a photon to pass a polarizer proportional to a sinusoidal function as in the orthogonal state no photon can pass. By the contrary in an aligned stat the probability to pass is 100%.]]

	If we conduct the [[Light_Polarization\|Polaroid]] experiment by doing a 180° scan, we will observe that the photons' probability of passage/transmission is proportional to a sinusoidal function, like a <math> sin^2(\theta)</math>. The sinus has to be squared as any probability can't be negative. Note that <math> sin^2(\theta)</math> is still a sinusoidal function.		If we conduct the [[Light_Polarization\|Polaroid]] experiment by doing a 180° scan, we will observe that the photons' probability of passage/transmission is proportional to a sinusoidal function, like a <math> sin^2(\theta)</math>. The sinus has to be squared as any probability can't be negative. Note that <math> sin^2(\theta)</math> is still a sinusoidal function.

@@ Line 1: / Line 1: @@
 [[File:Data Analise Polaroid.png|240|thumb| If we run the experiment for at least 90º of rotation is clear that we can expect a probability for a photon to pass a polarizer proportional to a sinusoidal function as in the orthogonal state no photon can pass and in an aligned stat the probability is 100%.]]
-If we conduct the "Polaroid" experiment by doing a 180° scan, we will observe that the photons' probability of passage/transmission is proportional to a sinusoidal function, like a <math> sin^2(\theta)</math>. The sinus has to be squared as any probability can't be negative. Note that <math> sin^2(\theta)</math> is still a sinusoidal function.
+If we conduct the [[Light_Polarization|Polaroid]] experiment by doing a 180° scan, we will observe that the photons' probability of passage/transmission is proportional to a sinusoidal function, like a <math> sin^2(\theta)</math>. The sinus has to be squared as any probability can't be negative. Note that <math> sin^2(\theta)</math> is still a sinusoidal function.
 Let's describe the polarization state of light as a two-dimensional vector, as illustrated in the figure. Vertically polarized light corresponds to a vector pointing upwards (0, 1), horizontally corresponds to (1,0). We use Dirac notation to represent these vectors, ''|V>'' and ''|H>'' respectively. An arbitrary vector can be written as \(|α〉=cos⁡(α) |V〉+ sin(⁡α) |H〉 \).
@@ Line 14: / Line 14: @@
 [[File:Light Polarization Diagram.png|240|thumb| Classical interpretation of light polarization. This interpretation is only possible for a immense number of photons, for a single or few ones we need to assume a quantize state associated with each photon.]]
 [[File:Multi Polaroid.png|240|thumb| In the case of several polarizers with a small incremental angle until the final one at 90º it can be showed that the probability for the photon to pass the cascade of polarizers became increasingly greater becoming 100% for an infinite number of polarizers!]]
 <!-- [[File:Experimental SetUp Polaroid.png|240|thumb| Set-up for the three polarizers paradox experiment.]]-->

← Older revision		Revision as of 13:28, 28 December 2024
Line 1:		Line 1:
−	[[File:Data Analise Polaroid.png\|240\|thumb\| If we run the experiment for at least 90º of rotation is clear that we can expect a probability for a photon to pass a polarizer proportional to a sinusoidal function as in the orthogonal state no photon can pass and in an aligned stat the probability is 100%.]]If we conduct the "~~Polaroide~~" experiment by doing a scan~~, lets say, of 180º rotation~~, we will ~~conclude~~ that the photons probability ~~should be~~ proportional to a sinusoidal function, like a <math> sin^2(\theta)</math>. The sinus has to be squared as any probability can't be negative. Note that <math> sin^2(\theta)</math> is still a sinusoidal function.	+	[[File:Data Analise Polaroid.png\|240\|thumb\| If we run the experiment for at least 90º of rotation is clear that we can expect a probability for a photon to pass a polarizer proportional to a sinusoidal function as in the orthogonal state no photon can pass and in an aligned stat the probability is 100%.]]
		+
		+	If we conduct the "Polaroid" experiment by doing a 180° scan, we will observe that the photons' probability of passage/transmission is proportional to a sinusoidal function, like a <math> sin^2(\theta)</math>. The sinus has to be squared as any probability can't be negative. Note that <math> sin^2(\theta)</math> is still a sinusoidal function.

	Let's describe the polarization state of light as a two-dimensional vector, as illustrated in the figure. Vertically polarized light corresponds to a vector pointing upwards (0, 1), horizontally corresponds to (1,0). We use Dirac notation to represent these vectors, ''\|V>'' and ''\|H>'' respectively. An arbitrary vector can be written as \(\|α〉=cos⁡(α) \|V〉+ sin(⁡α) \|H〉 \).		Let's describe the polarization state of light as a two-dimensional vector, as illustrated in the figure. Vertically polarized light corresponds to a vector pointing upwards (0, 1), horizontally corresponds to (1,0). We use Dirac notation to represent these vectors, ''\|V>'' and ''\|H>'' respectively. An arbitrary vector can be written as \(\|α〉=cos⁡(α) \|V〉+ sin(⁡α) \|H〉 \).

@@ Line 29: / Line 29: @@
 </math>
-where <i>Δθ=90º/N−1</i>.
+This simplifies to:
 <math>
 P_{total}=(cos^{⁡2}(Δθ))^{N−1}
@@ Line 39: / Line 39: @@
 Example:
-Suppose ''N=10'' polarizers are used to go from ''θ=0º'' to ''θ=90º''. Then, \( Δθ=90º/9=10º \)
+Suppose ''N=10'' polarizers are used to go from ''θ=0º'' to ''θ=90º''. Then, \( Δθ=90º/9=10º\).
-''Probability of passing each step:'' \( Pi=cos⁡^{2}(10º)≈0,97 \).
+*''Probability of passing each step:'' \( P_i=cos⁡^{2}(10º)≈0,97 \).
-''Total probability:'' \(P_{total}=(0.9698)^9≈0.75\)
+*''Total probability:'' \(P_{total}=(0.9698)^9≈0.75\)
 This result shows that gradual rotation increases the probability of transmission compared to using just two polarizers oriented at ''0º'' and ''90º'' directly, where no photons would pass at all as \(cos^{⁡2}(90º)=0\).

@@ Line 1: / Line 1: @@
 [[File:Data Analise Polaroid.png|240|thumb| If we run the experiment for at least 90º of rotation is clear that we can expect a probability for a photon to pass a polarizer proportional to a sinusoidal function as in the orthogonal state no photon can pass and in an aligned stat the probability is 100%.]]If we conduct the "Polaroide" experiment by doing a scan, lets say,  of 180º rotation, we will conclude that the photons probability should be proportional to a sinusoidal function, like a <math> sin^2(\theta)</math>. The sinus has to be squared as any probability can't be negative. Note that <math> sin^2(\theta)</math> is still a sinusoidal function.
-Let's describe the polarization state of light as a two-dimensional vector, as illustrated in the figure. Vertically polarized light corresponds to a vector pointing upwards (0, 1), horizontally corresponds to (1,0). We use Dirac notation to represent these vectors, ''|V>'' and ''|H>'' respectively. An arbitrary vector is written as \(|α〉=cos⁡(α) |V〉+ sin(⁡α) |H〉 \).
+Let's describe the polarization state of light as a two-dimensional vector, as illustrated in the figure. Vertically polarized light corresponds to a vector pointing upwards (0, 1), horizontally corresponds to (1,0). We use Dirac notation to represent these vectors, ''|V>'' and ''|H>'' respectively. An arbitrary vector can be written as \(|α〉=cos⁡(α) |V〉+ sin(⁡α) |H〉 \).
 Quantum mechanics explains how to calculate:
@@ Line 19: / Line 19: @@
 So, the photon behavior through a polarizer can be interpreted as:
-#Initial Polarization State: A photon approaching a polarizer has a specific polarization state, which can be represented as a superposition of the two basis states defined by the polarizer's axis, (i) paralleled aligned or vertical state and (ii) orthogonal or horizontal state.
+#'''Initial Polarization State:''' A photon approaching a polarizer has a specific polarization state, which can be represented as a superposition of the two basis states defined by the polarizer's axis, (i) paralleled aligned or vertical state and (ii) orthogonal or horizontal state.
+#'''Interaction with the Polarizer:''' Upon encountering the polarizer, the photon's polarization state is ''measured'' relative to the polarizer's axis. This process projects the photon's polarization onto one of two orthogonal components: (i) Parallel to the polarizer axis (transmitted) or (ii) Perpendicular to the polarizer axis (absorbed or blocked). The probability of the photon transmission is given by \(P_{transmit}=cos^{⁡2}(\theta)\), where <i>θ</i> is the ''angle'' giving the probability between the two states which in the classical theory resumes to the angle with the polarizer's axis.
-#Interaction with the Polarizer: Upon encountering the polarizer, the photon's polarization state is ''measured'' relative to the polarizer's axis. This process projects the photon's polarization onto one of two orthogonal components: (i) Parallel to the polarizer axis (transmitted) or (ii) Perpendicular to the polarizer axis (absorbed or blocked). The probability of the photon transmission is given by \(Ptransmit=cos^⁡2(\theta)\), where <i>θ</i> is the ''angle'' giving the prabability between the two states which in the classical theory resumes to the angle with the polarizer's axis.
+#'''Post-Polarization State:''' If the photon passes through, according to the probability, its polarization state is now aligned with the polarizer axis that it just pass by (it no longer retains its original polarization state, being this a key distinction from classical theory).
 Now if we have a chain of polarizers, ie if multiple polarizers are placed in sequence, with each successive polarizer rotated by a small angle <i>Δθ</i>, the total probability of a photon passing through all <i>N</i> polarizers is:
@@ Line 41: / Line 39: @@
 Example:
-Suppose ''N=10'' polarizers are used to go from ''θ=0º'' to ''θ=90º''. Then, \(Δθ=90º/9=10º\)
+Suppose ''N=10'' polarizers are used to go from ''θ=0º'' to ''θ=90º''. Then, \( Δθ=90º/9=10º \)
- Probability of passing each step: \(Pi=cos⁡^{2}(10∘)≈97%\).
+''Probability of passing each step:'' \( Pi=cos⁡^{2}(10º)≈0,97 \).
- Total probability: \(P_{total}=(0.9698)^9≈75%\)
+''Total probability:'' \(P_{total}=(0.9698)^9≈0.75\)
-This result shows that gradual rotation increases the probability of transmission compared to using just two polarizers oriented at ''0º'' and ''90º'' directly, where no photons would pass at all as \((cos^{⁡}2(90∘)=0)\).
+This result shows that gradual rotation increases the probability of transmission compared to using just two polarizers oriented at ''0º'' and ''90º'' directly, where no photons would pass at all as \(cos^{⁡2}(90º)=0\).
 Key Points of Clarification:
-*The photon does not "keep" its original polarization if it passes through; rather, it becomes aligned with the polarizer axis.
+*The photon does not ''keep'' its original polarization if it passes through; rather, it becomes aligned with the polarizer axis.
 *The outcome is probabilistic: a photon may or may not pass a polarizer, based on the projection of its initial polarization onto the polarizer's axis.
 *This phenomenon underscores the quantum mechanical principles of state collapse and measurement, distinct from classical wave explanations.